Are you going to try to tell me that something infinitely close to 1 isn't 1?
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Are you going to try to tell me that something infinitely close to 1 isn't 1?
yesQuote:
Originally Posted by Kushna Mufeed
Yes.
EDIT: xD Ynot got to it first!
Prove it
for practical examples, 0.9 recurring does equal 1, because machines have a fixed amount of space in which to store a valueQuote:
Originally Posted by Kushna Mufeed
give it an irrational number like 0.9 recurring, and it'll fill up the space, and still have a remainder, so it'll round up to 1, but this is not accurate
0.9 recurring is, by definition, a number that infinitely reaches towards 1 but never gets there.
So that question really has no place.
No one asks whether 1 equals to 2...we know that each is a different number by definition, as it were. So why ask whether 0.9 recurring (that very number) equals to 1 (a different number) if you've just spoken about two different numbers? Not variables but different real numbers.
Just because it's used as equaling 1 for calculations doesn't make it precise and true. Sounds ridiculous but...you can't argue with the number's very definition, and apparently people prefer actually finishing their calculations rather than sitting there at a dead end unable to work with an irrational number that never ends.
I hate math though, so I'm just going at this from a logical point of view. Definitions are axioms!
another way to look at it
0.15 is a rational number
but write that in hex, and you get 0x0.2666666.....
an irrational number
a rational number in one base can be irrational in another
and vice versa
there will likely be some base where decimal 0.9 recurring is rational
and therefore easily shown that it is not equal to 1
:( I was going to say something like that.Quote:
Originally Posted by Ynot
Actually, you're wrong. Firstly, people have asked for a proof that 1 does not equal 2, and all the other stuff assumed in arithematic.Quote:
0.9 recurring is, by definition, a number that infinitely reaches towards 1 but never gets there.
So that question really has no place.
No one asks whether 1 equals to 2...we know that each is a different number by definition, as it were. So why ask whether 0.9 recurring (that very number) equals to 1 (a different number) if you've just spoken about two different numbers? Not variables but different real numbers.
Just because it's used as equaling 1 for calculations doesn't make it precise and true. Sounds ridiculous but...you can't argue with the number's very definition, and apparently people prefer actually finishing their calculations rather than sitting there at a dead end unable to work with an irrational number that never ends.
I hate math though, so I'm just going at this from a logical point of view. Definitions are axioms!
1=0.9999...
http://en.wikipedia.org/wiki/0.999...#Proofs
It has been proven, look above. Also, 0.9999.. by definition is not irrational.
See 1/3=0.3333....., then you times it by 3/3=0.9999....
Actually, even if you couldn't do that it still has a repeating digit, which proves it can't be irrational, as the definition of a irrational number is that there is no repeating digit in sequences of numbers in n-1 turns. For example you don't get stuff like 2.12222..., this would have a repeating 2, so wouldn't be irrational. 0.999.. has repeating 9 so is not irrational.
P.S. Seriously, don't do mathematics.
It has been mathematically prove, look above. That 0.9999... =1, so its a fact or a theorem in this case.Quote:
there will likely be some base where decimal 0.9 recurring is rational
and therefore easily shown that it is not equal to 1
Wrong.
y = x^3 / x - 5(.999~)
If 1 = .999~ then y would be undefined at x = 5. When x = 5, that equation equals -5. You have to use limits to show it, but it's -5, not undefined.
Limits is a weird thing. Those proofs are correct on wiki, however you can also prove that they don't work. This happens a lot with limits and calculus.
the (1/9) x 9 proof was proven inaccurate
it's essentially using a property of mathematics to disprove that same property
there's a counterpoint that says,
it should be written as (I'm paraphrasing)
(1 / 8.999999.....) x 8.99999.....
which is not possible to do (with absolute accuracy)
so 0.99999.... cannot equal 1
Proof doesn't work. Seriously, are you some sort of mathematical crank.Quote:
Limits is a weird thing. Those proofs are correct on wiki, however you can also prove that they don't work. This happens a lot with limits and calculus.
A proof is a proof, it has been proven. It is a theorem, it is a fact. Anyway, the only thing strange is that
Quote:
Tom Apostol concludes,
The fact that a real number might have two different decimal representations is merely a reflection of the fact that two different sets of real numbers can have the same supremum
The problem with numbers is that people look at them differently depending on how they are used. Not in terms of rounding, just in terms of how they get used in calculations.
Does .999~ = 1?
Computers - yes
Physics - yes
Relativity Physics - no
Math - no
Calculus - yes
Does -0 = 0? (another common dispute)
Computers - no
Physics - no
Relative Physics - no
Math - yes
Calculus - yes
If you'd like I can give examples of all of these.
Firstly, NO. 9.99999=10, not that 8.999999=10.Quote:
it's essentially using a property of mathematics to disprove that same property
there's a counterpoint that says,
it should be written as (I'm paraphrasing)
(1 / 8.999999.....) x 8.99999.....
So lets 1/1=9/9, everything is okay, then we have 9x1/9=1, then we have
9x 0.111...=1, therefore 0.99999=1.
Anything divide by something is 1, so how is that a counterpoint?
Lastly, it has been prove by analysis, so there. Look at the bottom of the wiki article.
Calculus is mathematics, also you can use analysis to prove it. So what are you basing you're assumptions on. It has been proven in mathematics that 0.99999...=1.Quote:
Math - no
Calculus - yes
You can prove it using constructionism, which is most concrete form of mathematics. You can construct it from the real numbers, or prove it by dedekind cut.
Wow, I used to think Ynot was an intelligent person. And here he is saying that .99... does not equal 1.
It does.
There are numerous proofs that .99... equals 1. How many proofs are there that it does NOT equal 1? Zero. There are no such counter-proofs.
Here is a proof. Try to think of a number between .9999... and 1. Thought of a number? No? That's because there are no numbers between .999... and 1. You know why? Because they're the same number. If they were not, then there would be a number between them.
This isn't rocket science. I've known this since middle school.
http://polymathematics.typepad.com/p...sorry_it_.html
One of many sites that you could learn from.
PS: Please stop posting your flawed mathematics in this thread. It is an embarrassment. Ynot, stop posting here unless you cure your ignorance.
See my post above about multiple views.
Computer science says that 1/∞ = 0 so 1 - 1/∞ = 1
Physics says the same thing because it uses limits to reach asymptotes
Relative physics uses calculus which can reach asymptotes, but doing so causes failure among basic physics so the break down of physics is what says that .999~ != 1, not the math.
Simple math states that asymptotes can not be reached, therefore .999~ != 1
Calculus can use limits to reach as asymptotes
Mathematics says you can do a dedekind cut and then show that 0.9999...=1. There is various mathematical proofs that this is true. Go look at the wiki article. Also, you can prove it by constructing the real numbers from axiomatic set theory. The point is, there is no counter proof, all you have is faulty reasoning.Quote:
failure among basic physics so the break down of physics is what says that .999~ != 1, not the math.
Simple math states that asymptotes can not be reached, therefore .999~ != 1
Calculus can use limits to reach as asymptotes
Also, do you except that geometric convergence in mathematics, for example 1/2+1/4+1/8+...=1. If so then you except that 0.999...=1. As all you need is r=1/10 and then have
9(1/10)+9(1/10)^2+....=1. Hence all you need to except is geometric convergence, which is accepted within mathematics.
There is something called analysis, seriously do you know any analysis? or how to prove stuff within analysis?Quote:
Calculus can use limits to reach as asymptotes
Actually, 0.9~ is by definition equal to 1 because of the axiom that every real number has two representations; in this case 1.0~ and 0.9~.Quote:
Originally Posted by Merlock
this forum needs a math section for all the nerds out there who think math is philosophy!
Math is to Philosphy as Binary is to Computer Programming.
When I punch 0.9999999999 in on my TI-34 II, it returns 1 when equal is pressed. 0.9 repeated only appears to equal 1 because machines round it up.
That's a finite sequence of 9s. This is in the case of an infinite sequence.
This. Topic. Ismakingmecringe. Especially the logic about "it is really .999, but machines round up."
The arguments I would bring in have already been noted (I thought I'd never "Thank" wendylove until today).
Anyway, XKCD forum is planning on trolling the place tomorrow. Look what you've done.
I welcome them with open arms.
ERTW
EAM (Engineers are morons).Quote:
Originally Posted by Kushna Mufeed
This has nothing to do with physics or computer science, this has to do with MATHEMATICS and the FACT that .999 repeating is EQUAL TO ONE.Quote:
Originally Posted by ninja9578
Please get SOME idea of what you're talking about and stop posting bullshit.Quote:
Relative physics uses calculus which can reach asymptotes, but doing so causes failure among basic physics
.999... IS NOT AN ASYMPTOTE. IT IS A NUMBER. ONE WHOLE NUMBER.Quote:
Simple math states that asymptotes can not be reached, therefore .999~ != 1
Just like 1 is not an asymptote, 3 is not an asymptote, .5 is not an asymptote.
Does 3.0000... not exist because the number's an asymptote? Is that number "going anywhere"?
1/3=0.333333 ect
1/3 * 3 = 1
0.333333 * 3 = 0.9999999
1= 0.9999999
Or something along those lines despite not being true meh...
Where's Merlock when you need him.
So are you claiming that .99 repeating does not equal 1 after offering a very basic and self-explanatory proof of it?Quote:
Originally Posted by NeAvO
That's like showing someone an apple and saying "this apple is not an apple."
News flash: .99... does equal 1. Nothing you say can change a very simple truth of math.
Wait, what?Quote:
Originally Posted by ninja9578
I thought -0 = -1(0) = 0
And technically, .3333...(3) doesn't equal 1, but 1/3(3) does.
well, I'm always willing to be proved wrong
I still don't agree (and quick google says I'm not alone)
http://www.math.fau.edu/Richman/HTML/999.htm
I'm not a mathematician, but I'm not as naive as to think there's a definitive answerQuote:
Arguing whether 0.999... is equal to 1 is a popular sport on the newsgroup sci.math---a thread that will not die. It seems to me that people are often too quick to dismiss the idea that these two numbers might be different.
oh, and as for the name calling.....grow up
When I discovered this .999 problem it made me realize the true stupidity of rational thought.
If something is infinitely close to something else, isn't it touching it?
No, because the universe doesn't work in a way that makes sense. When do we get to do it over again?
if 0.999~ = 1
does, 0x2.666~ = 0x2.7
?
It equals 1.Quote:
Originally Posted by A Roxxor
Google also says this: http://www.google.com/search?hl=en&s...at&btnG=SearchQuote:
Originally Posted by Ynot
In this case there is.Quote:
I'm not a mathematician, but I'm not as naive as to think there's a definitive answer
You can't "twist" it because you are saying that a != a. There is simply no way this can be true with the laws of our universe. .99... is equal to 1, a = a.
Learn up, and don't come to a thread to spread your worthless ignorance and ill-informed ideas. I can't even take you seriously anymore, because of the utter nonsense you've been posting.Quote:
oh, and as for the name calling.....grow up
Except we're talking about mathematics and the fact that .99.. repeating is equal to 1 through simple mathematic proofs. There is no philosophy here. a = a, it really is that simple.Quote:
When I discovered this .999 problem it made me realize the true stupidity of rational thought.
If something is infinitely close to something else, isn't it touching it?
No, because the universe doesn't work in a way that makes sense. When do we get to do it over again?
Besides, you clearly don't understand the nature of infinity. I can explain if you're actually willing to listen, which appears to be a long shot.
If you can prove it, yes. Is that hexadecimal? Then you can't prove it, because it's not true. That notation I'm not familiar with though and it seems to be that you are continuing to spam nonsense.Quote:
does, 0x2.666~ = 0x2.7
you know what,Quote:
Originally Posted by hungrymanz
screw you
.33333... * 3 = .99999...
1/3 * 3/1 = 3/3 = 1
.9999... Would be more like an asymptote. Approaching a number to infinity, but never reaching it.
Learn to argue. Learn to do sixth grade math. And screw you too.Quote:
Originally Posted by Ynot
Yes it does.Quote:
And technically, .3333...(3) doesn't equal 1
Yep, a proof that 1 = .999...Quote:
.33333... * 3 = .99999...
1/3 * 3/1 = 3/3 = 1
Not very hard to prove that.
Edit:
Is 1/3 infinitely close to .333... ? Yes. Is it also equal to 1/3 and .333... ? Yes (unless you insist on arguing elementary mathematical truths). "Infinitely close" is congruent to "equal to" - it is the nature of infinity. Newton understood this, 400 years ago. Why can you not understand it today?Quote:
If something is infinitely close to something else, isn't it touching it?
Sort of.
Let's try this, though:
.9999... != 1, because, actually, it's .3333...(3) that equals one, which means that .3333... != .9999...
You have been disproved.
This is true.Quote:
Originally Posted by A Roxxor
You are right.Quote:
which means that .3333... != .9999...
But how does that lead to this conclusion:
Quote:
.9999... != 1
I appreciate your attempt at an argument but don't be so arrogant as to claim that I have been disproved, when there are clearly huge holes in your argument.Quote:
You have been disproved.
Because .9999... = 1 = .3333...(3). So .9999... Can't be equal to 1.
1/3 = .3333...
3(1/3 = .3333...)
3/3 = 1
1 = 1
^I'm with stupid
You contradict yourself:Quote:
Originally Posted by A Roxxor
I'm not sure what you're misunderstanding, perhaps you have a skewed understanding of the transitive property?Quote:
So .9999... Can't be equal to 1.
No...
Look at this, instead:
1/3 = .3333...
3(1/3 = .3333...)
3/3 = 1
1 = 1
Let me put this in plainer terms...Quote:
Originally Posted by Kushna Mufeed
I was wrong, before.
You say that .999... = 1 because 1/3(3) = 1
Actually, that's not true.
1/3(3) = 1 because .3333...(3) = 1.
.9999... != .3333...(3), thus is not equal to 1.
But then:
x = .99...
100x = 99.99...
99x = 99
x = 1
:P
And then:
.9999... =
.9999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999 99999999999999999999999999....
Which is not 1. Never will be 1. Dividing a repeating decimal like this by ten forever doesn't magically make it equivalent 1, it just makes it infinitely precise.
You can argue that it's not one with words and exagerated logic all day long. But no matter how many fancy words you have, numbers say that .9~ is 1. Numbers do not lie. Words do.
Survey says....
ONE!
So nanananabooboo to the implied circular logic.
Hungrymanz, you just NEED it to be 1 so the universe can exist in a logical, fluid way.
It doesn't.
Theoretical mathematics do exist in a logical way, however.
Why are so many people here ignorant of their lack of qualification to solve this problem?
0.999999... = 1, yes.
One proof has already been given; x10, -1x, /9x, you get 1.
I can probably do it another way using the sum formula for a geometric progression, a/(1-r):
∞
Σ9/10 x 1/10^n = (9/10) / (1 - 1/10) = (9/10) / (9/10) = 1
0
There.
Many people here have failed to realise that mathematics is not 'real' or 'tangible'. It is a set of rules which tell you how to manipulate symbols to get a set of truths about those symbols. Within that system, there is NO contradiction about the fact that 0.999... = 1.
How can a number be "approaching" anything? It isn't changing; it's a number. It's not a function. It's a single number. You must realize that 0.9~ is not a process of adding 9's, it's the totality of an infinite number of 9's after the decimal, and that is why it does equal 1.Quote:
Originally Posted by A Roxxor
That was an incorrect proof by the way (if that's what it was supposed to be) because you would then need to prove that 0.333... = 1/3, and you're faced with exactly the same problem (although again it is trivial to do properly: x10, -1x, /9; or use my summing method above).
What?Quote:
Originally Posted by drewmandan
That's what makes .9 different from .999...
(1/3 = .33...)(3)
1 = .99...
Or
1 = 1
?
Wouldn't the first one be untrue?
...interesting maths? :/
Neither of those statements are untrue. 1 = .99... = 1 = 1, if you like... if I understand what I think you're trying to say correctly, then I don't think you've quite mastered the equals sign.
.99... is effectively an alternate way of writing 1.
I'm only in Algebra II...
What I mean is:
.333... is 1/3 in decimal form. If you multiply it by 3, you get 1, not .999..., right?
And are there types of decimals like this?
2.99...3
Where 3 follows an infinite amount of repeating nines. At the end of infinity.
.333 = 1/3
.999 = 1
The = sign indicates that these things are equal. So
.333 x 3 = .999;
.333 x 3 = 1;
1/3 x 3 = .999;
1/3 x 3 = 1
Maybe writing out the permutations will help you get it.
There are no decimals like the ones you gave above. Technically I don't see why you couldn't express them mathematically, but it would be pointless, as the numeral at the end would be equal to 0, and so your decimal above = 2.99... = 3.
I get that. I'm not stupid.
2 = 5 is an incorrect statement. If you come to that for an equation, the equation has no solution in algebra.
Do you understand what I was asking now?
There are no equations which would lead to that conclusion.
2 = 5 is not like the above because 2 is in fact not 5.
Yes, I just tried.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 .9999999~9 1
THEREFORE it is not even close to equal 1. 0.9999~9 is a different number. Ever hear of the density property?
There is no way of expressing .9... as a fraction other than 1/1.
No, 1/1 is a whole...1.
wtfQuote:
Originally Posted by xXSomeGuyXx
my number line failed sorry
But .999... is exactly 1.
No, .9999999~9 is .999999999~9. 1 is 1.
So then express .999... as a fraction.Quote:
Originally Posted by xXSomeGuyXx
It is a rational number, so this should be simple, right?
.999... = 1.
We're not talking about 0.9...9. We are talking about an infinite number of 9's. What you wrote has a termination.Quote:
Originally Posted by xXSomeGuyXx
The big problem I have with these proofs is that you are applying rules meant for rational numbers on irrational ones.
For example: 10*0.99999999... = 9.9999999999... would normally move the 9 out of the last place value and so in a rational number you get
10*0.999 = 9.99
When we do the next step, that 9 we would moved right gets subtracted and we're left with 8.991 Of course, the trick is to say "theres infinate numbers of nines, lets ignore that" but in reality, it should end up being something like
9x = 8.999999999(infinite times)99991 and thus x = 0.9999999... still
You can't apply those sorts of rules to irrational values. You'd have to leave it as un-evaluated like:
10x = 10*0.99999999...
The big problem I have with people arguing that 0.9~ =/= 1 is that their math education is so lacking that they don't even know what a fucking rational number is.Quote:
Originally Posted by arby
0.99... isn't irrational...
I don't know what you were doing. This, maybe?
10x = 9.9...
x = 0.9...
Subtract.
9x = 9
x = 1
arby; Well, you don't normally find decimals in proper maths.
However if you define them properly as I did above with sigma notation, there is absolutely nothing wrong with the proof.
.999... is not irrational, by the way. Even if it was irrational, you can perform all the usual operations on it.
I know. It's like calling me Grod. Grod is Grod. I'm SomeGuy.
A number is a number. If you round up, (which means you suck at maths) then it equals 1.
If you think .99999~99 equals 1, you're high.
But it's just been proved for you in two different and valid ways.
Then what is the fractional equivalent of .999...?
No one said that number equals one. We said 0.9~ equals one. See, the way you wrote your version of the number, it's obvious that you think the 9's "end". They don't. As soon as you understand that, you will see that it clearly is 1.Quote:
Originally Posted by xXSomeGuyXx
Also, here's something to consider.
1/3 in base 10 is 0.3~
1/3 in base 6 is 0.2000~ (in other words, just 0.2. Do the long division if you don't believe me)
Then, in base 6, if you do 3 * 0.2, you get 1.
This would suggest that there's no fundamental difference between numbers with an infinite number of non-zero repeating decimals and an infinite number of zeros. Therefore, it would seem that the "1/3 proof" is, in fact, quite valid.
I also have 6 ways to prove that it, in fact, is not 1.
1. They have different points on a number line.
2. .999~ in a fraction is .999~/1
3. .999~ + .111~ =1
4. Density property ;)
5. Rounding up doesn't count
6. The lines y=1 and y=.999~ are on different positions.
Nooo, i understand that repeating decimals don't end. I can stop writing it that way.Quote:
Originally Posted by drewmandan
But if you took the time to actually plot them on a number line, they would have seperate positions.
You'll find that almost all of those are actually only true if you first assume that .999 is not 1.
Except this one:
3. .999~ + .111~ =1
Which shows that you don't know what you're talking about at all. .999... + .111... is definitely not equal to 1. It's equal to 1.11...
Do it on a calculator if you don't believe me.
.999... + 0.00...1 recurring is 1, and 0.00...1 is 0, so .999 = 1.
2. Now get rid of the decimal.Quote:
Originally Posted by xXSomeGuyXx
4.
You fail at algebra.
.999...x = 1
x = 1/.999...
x = 1
Again, x = .9...; 10x = 9.9...; 9x = 9; x = 1
@ Xei
Whoops, sorry. That doesn't make sense. I just did that on my calculator, and I give you that one.
In case you haven't noticed, that post was edited...:PQuote:
Originally Posted by A Roxxor
And I don't fail at algebra.
@ Xei, what's wrong with the Density Property reason?
Whait...what? If you take away the decimal, it's not the same number. That doesn't make sensu unless you divide the answer by...1000.Quote:
2. Now get rid of the decimal.
4.
You fail at algebra.
Well all of your other 'proofs' are wrong because you first have to assume that .999 is not 1 in order for them to work. Try it.
I've never heard of density property and Wikipedia has nothing to say about it.
Well, your first last proof didn't make any sense :PQuote:
Originally Posted by xXSomeGuyXx
And y = .999... is the same as y = 1. Because .999... = 1.
:P
If you took the time (IMPOSSIBILITY AHEAD!!!) to make a graph with every single decimal between 0 and 1 and the graphed y=.999~ and y=0, you would see that they are on different positions. Especially if you made the intervals big enough. Picture it. Please.
y=1 you mean.
And no. There would be an infinitely small difference between them.
Imagine you've got a meter rule where 0cm is marked 0 and 100cm is marked 1.
How many times bigger would you have to make the meter rule so that the distance between 0.999... and 1 was 1cm wide?
depends on how you mark the points.
There's no ambiguity at all about my question.
Lol, we've been at this for pages!
7. .999~ doesn't even look like 1!
lolwut?
How is that rational? A rational can be written as p/q where p and q are both integers.
How do you write 0.99999... as p/q?
The density property is one way of proving .99... equals 1, and not a way of disproving it.
http://mathforum.org/library/drmath/view/56025.html
If .999... and 1 are different numbers, then I challenge you to find a number between them. That would effectively prove that they are different numbers.
No matter how you try, you wont' find any numbers between them.
9/9. Surely you know that a number like 45/99 is equal to .45454545... with the 45's repeating. Likewise, 7/9 is .777....Quote:
Then what is the fractional equivalent of .999...?
9/9 is .999... and, unless you're mathematically challenged, equal to 1.
.999... is not irrational. An irrational number is a number with a non-repeating, non-terminating decimal. I'm pretty sure .99... is a repeating decimal.Quote:
Originally Posted by arby
Besides, by your logic 5 is an irrational number. Since 5 = 5.000....
You do:Quote:
And I don't fail at algebra.
Quote:
.999~ + .111~ =1
I don't need anything to be anything, .99.. equals 1 because it does, and not because anyone needs it to. You're posting stupid comments.Quote:
Originally Posted by Omnius Deus
You're right. There is no logic in the universe. Every single logical deduction you've ever made is wrong. Please stop using logic and go join the animals in the wilderness. Logic is not for you. Your universe is not logical, apparently.Quote:
It [the universe] doesn't [exist in a logical way].
I, and several others, have proved that .99... equals 1. As yet there have been no correct proofs to the contrary.
This is like saying that 2 != 6/3 because, actually, it's 4/2.Quote:
Originally Posted by A Roxxor
Are you trolling?Quote:
7. .999~ doesn't even look like 1!
10 doesn't look like 1+2+3+4.
You're not a mathematician. A few of the people here are.Quote:
lolwut?
How is that rational? A rational can be written as p/q where p and q are both integers.
How do you write 0.99999... as p/q?
It can be written as 1/1.
5*1 + 3*2 - 3*3 != 2Quote:
Originally Posted by xXSomeGuyXx
by your own logic.
He's referring to the fact that the reals are constructed from Cauchy sequences of rational numbers, and it's said that the reals are "dense in the rationals" because a real number can be found between every two distinct rational numbers. Ironically, the density of the reals forms the basis of the analysis-based proof that 0.9~ DOES equal 1:Quote:
Originally Posted by Xei
http://en.wikipedia.org/wiki/0.999#Analytic
Who said 0.9~ = 0? I don't remember saying that.Quote:
Originally Posted by xXSomeGuyXx
Rational numbers are numbers that, in decimal form, either repeat in a pattern or terminate. 0.999... is rational.Quote:
Originally Posted by arby
Exactly :PQuote:
9/9 is .999... and, unless you're mathematically challenged, equal to 1.
If only we had 6 fingers on each hand instead of 5, and had a mathematical system based on the number 12.
Mine are in bold.Quote:
Originally Posted by hungrymanz
No. They are fractions of whole numbers.Quote:
Rational numbers are numbers that, in decimal form, either repeat in a pattern or terminate. 0.999... is rational.
0.999~ doesn't terminate.
I wish you'd terminate.
SomeGuy you are deliberately trolling.Quote:
You are wrong. 9/9 is one. .999~/1 = .999~. Yes you are correct 9/9 equals 1, but 9/9 does not equal .999~.
1/9 = .11...
2/9 = .22...
etc etc
9/9 = .99...
9/9 also = 1
We've shown this dozens of times. For instance 3/9 = 1/3 = .33...
1/3 * 3 = .33... * 3 = 3/3 = 1 = .99...
I proved .999... = 1 whereas God has not been proved.Quote:
Oh, because that REALLY makes sense. God exists because he does.
Okay, okay, okay.
I believe .999~ is .999~.
I believe 1 is 1.
Xei, i don't want you to terminate. Then we can't debate about 1!
What?Quote:
Originally Posted by Xei
2 is a rational number.
This is 2 in decimal form: 2.
It terminates. Thus, it is rational.
No, but it does repeat.Quote:
Originally Posted by xXSomeGuyXx
-------------
Look at this:
2.999... = 3. There are no numbers between those two.
Again:
x = 2.9...
10x = 29.9...
Subtract the first equation from the second:
9x = 27
x = 3
Therefore, x.999... = x + 1 and .999... = 1.
Right.
All rational numbers can be written as whole number fractions. For example 4/2 = 2. Pi is irrational, and cannot be written as a fraction.
It doesn't matter what you believe. .99... = 1 and this can be (and has been) proved. Whether or not you believe it doesn't change reality.Quote:
Originally Posted by xXSomeGuyXx
I'm not a troll. I'm having a debate. Plus, I actually am a nice guy. Trolls suck.
You are spouting random crap about a topic you're obviously ignorant about. If that's not trolling that's just plain immaturity.Quote:
Originally Posted by xXSomeGuyXx
The definition of a rational number is that it is a fraction of two whole numbers. Decimals have no place in pure maths.Quote:
What?
2 is a rational number.
This is 2 in decimal form: 2.
It terminates. Thus, it is rational.
Your definition includes things like 0.12112211122211112222... which is not rational. In fact it's not even irrational.
You can also see the proof in certain graphs. 1/x-1 for example cannot equal 1, but its value rises or drops indefinitely as it approaches the asymptote. And no matter how close the value gets to 1 (in other words, how many times 9 is repeated), it is never equal to one.
Asking if .9999999~ repeated is equal to a rational number is like asking the same of infinity. The answer is that it's not a number to begin with, but an irrational system: a term we use to stand for something our minds couldn't normally contend with. Sort of like how we use i to stand for the square root of a -1 (which can't exist, but it's still an essential component of mathematics).
No, no. I mean repeating. Not patterns. Sorry, wrong word.Quote:
Originally Posted by Xei
0.12112211122211112222 is irrational, because it doesn't repeat, and it doesn't terminate.
And yeah, I was just stating the definition I knew. You said "Fractions of whole numbers", which threw me off.
Okay, I know absolutely nothing about maths. And I'm not immature. Trolling? Because I believe something else than you do, and am trying to prove it, you think I'm trolling? Yeah, okay. Remind me never to have a debate with you.Quote:
Originally Posted by hungrymanz
NO.Quote:
Originally Posted by Tamias.Squirrel
ABSOLUTELY NOT.Quote:
The answer is that it's not a number to begin with, but an irrational system:
1/3 is clearly a real, rational number. Look at its decimal representation:
.333....
IT IS A NUMBER. Irrational system? It is one single number. It doesn't do anything. It is as solid as 2 or 3 or 1/5 or 3/7.
You can't take a third of a pie and then say that pie's calculating itself out to infinity. You just have a third of a pie. And if you have three thirds, you have one whole, equal to .999... of the pie.
Fine by me.Quote:
Remind me never to have a debate with you.
Rational numbers either terminate or have repeated decimals.Quote:
Originally Posted by xXSomeGuyXx
Here's a couple that cropped up in my second year astronomy. Good. Fucking. Luck.Quote:
Originally Posted by xXSomeGuyXx
5[exp(x)-1] = x*exp(x)
and
(G*M*m) /((r–R)^2) – (G*m*n) /(R^2) = (m*v^2)/(r–R)
where your goal is to solve for big R as a function of G, M, m, n, v, and r, which can be taken as constants.
O_O See ya in a few weeks...lol. Those actually look fun.
That's actually a good point xD Hmm... This is a lot more complicated than I first thought. Maybe we should all just agree that nobody really knows?Quote:
Originally Posted by hungrymanz
Lol, sure.
Hint: There's no exact answer for either of them. Kinda blows your mind if you think about that fact.Quote:
Originally Posted by xXSomeGuyXx
EDIT: One thing. The first equation has a trivial solution x=0. I want the non-trivial solution.
No, we do know. It has been proven dozens of different ways, including real number construction, the be-all end-all proof of numbers, that 0.9~ DOES EQUAL 1.Quote:
Originally Posted by Tamias.Squirrel
What about this?
There are no numbers between 1.000...1 and 1, right?
So they are the same, because adding the one to the end is redundant.
So basically, .999... is just 1 - 0.000...1, which is zero, making .999... 1.
Well, yeah., Ima go use a table of solutions.
He is right. Maybe you don't understand it, Tamias, but there are people who do. I encourage you to keep trying to understand it.Quote:
Originally Posted by drewmandan
Question, exp(x) is to the xth power, correct?
exp(x) is e^x, where e is the usual eQuote:
Originally Posted by xXSomeGuyXx
But it doesn't: Like I said before, the graph 1/x-1 gets infinitely close to 1, but never, ever touches it. The y-values just keep going up or down. So no matter how close to one you 1, you are never exactly on 1.Quote:
Originally Posted by drewmandan
http://img265.imageshack.us/img265/2540/dsc01213xb3.jpg
I guess I don't get it.
Do you mean 5e^(x+1) = x.e^x ?
Or 5e^x + 5 = x.e^x?
Neither of these has solution x=0.
Learn2distribute minus signQuote:
Originally Posted by Xei
5[exp(x)-1] = x*exp(x)
Meaning 5*e^x - 5 = x*e^x, which has a solution x = 0.
What is this? Proof by screen shot? Wtf? By the way, 1/(1-x) has nothing to do with the constant number 0.9~. At all.Quote:
Originally Posted by Tamias.Squirrel
You have to understand that .999... is a number, not a function or a graph.Quote:
Originally Posted by Tamias.Squirrel
I understand that, hungrymanz.
What I don't understand is why this thread continues and people still view the issue as debatable despite being shown the 'proof' that they are the same. It is... fact. It's really that simple. Whether or not it makes sense is irrelevant.
Your logic on the issue is irrevelant.
Human logic means nothing next to numbers!
You are all powerless next to the awsome might of calculus! Understand?
IF:
G = 5
M = 6
m = 6
R = 5
r = ?
n = 6
v = 3
:
(G*M*m)/((r-R)^2))-G*M*n)/R^2 = (m*v^2)/r-R
r = 0.405218595
Unless I'm doing it wrong.
wtf
Anyway that exponential equation only has one solution.
You're doing it wrong. I said to get big R as a function of all the constants. I didn't say you could just arbitrarily throw in numbers willy nilly.Quote:
Originally Posted by xXSomeGuyXx
It's got 2. One at 0 and another greater than 0.Quote:
Originally Posted by Xei
OH! Okay. That makes sense nao. Shit...
You're right, it does have a solution just under 5, and I've got no fucking idea how to get rid of the fucking lns and I feel very inadequate right now.
Lol.
I think in general xe^x=1 might be impossible to solve properly?
It can be done by iteration... but not precisely?
I'm stuck on
For example, not real problem:
4=[44456.55^x]x
Quote:
Originally Posted by Xei
These are both the same basic equation. And yes, x can't be solved for explicitly. And R can't be solved for explicitly in the other example. I chose those examples to prove that not all equations can be solved :)Quote:
Originally Posted by xXSomeGuyXx
So, they are impossible?
Grr... I just felt as if everything I'd ever learnt was falling from under my feet. :(
Does this mean the roots are transcendental? Well, considering the expression contains e I suppose it'd be hard for them not to be; but would it still be the case if the equation contained 2^x?
I sucked my brain juice dryon those two!!! GRRR I agree with Xei.
Not to worry, the roots can be expressed as convergent series. And yes, any base other than 1, (-1,) or 0 gives roots that can't be expressed in closed form.Quote:
Originally Posted by Xei
Aha, that density proof proves it. There is no number between the two so they are not distinct reals. </thread>
So yes, I will concede that 0.9999... = 1
But I still do not agree with the algebra method of proving it. Especially the one that uses 0.33333.... The other one is up in the air but I don't really care.
And yes, Xei, I am a math student. First year majoring in comp. sci. at waterloo. But I HATE pure math =/
0.999~ == 1
but
0.999~ !== 1
I think that satisfies all sides, no? :D
var ag = "Agree"
function lol(){
if(world.explode==false){
xXSomeGuyXx.agree();
}
else if(world.explode==true){
world.explode();
print("WOW");
}
}
lol()
xXSomeGuyXx = ag.Ynot
Grod+9=Whales
Ynot/Me=Grod
You're entitled to think what you want. Just don't expect to be correct.Quote:
Originally Posted by arby
IMO !== is just stupid, PHP should've stuck with !=Quote:
Originally Posted by Ynot
what it boils down to is
does having the same value make something Equal?
(that's equal with a big E)
Well = is an assigning operator, == is a comparing operator. I think !== makes more sense, don't you?
3 != 4
(not equal in value)
3 == 3.0
(equal in value only)
3 !== 3.0
(equal in value, but not in context)
3.0 === 3.0
(equal in value, and equal in context)
*edit*
is having the same value the only thing that makes numbers Equal?
That actually is quite awesome, I retract my previous statement.Quote:
Originally Posted by Ynot
That's programming for ya'.
LOLQuote:
Originally Posted by Ynot
awesome
Oww my head...
Hmm... I'll ask my pre-calc teacher on Monday.
And out of curiosity, when was the last time someone on DV admitted they were wrong?
Me, couple ofhours ago.
I did not too many posts back...
5(e^x-1)=x(e^x)Quote:
5*e^x - 5 = x*e^x
5=x(e^x)/(e^x-1)
ln5=lnx + xln(e) - ln(e^x-1)
ln5=x+lnx-ln(e^x-1)
5(e^x-1)=xe^x
Back to square one.
(5-x)e^x=5
x=ln5-ln(5-x)
x+ln(5-x)=ln5
x=0 and
x<5
I think, you can only solve it using numerical methods.
let x=-xQuote:
xe^x=1
so
-x=e^x
then
e^x+x=0
I'm pretty sure you're correct Xei.
P.S. Xei have you done UCAS, what uni's have you applied too. I have applied too, Oxford, Manchester, Warwick, York and Bristol. However, I haven't got any offers yet, but I have got an interview with Manchester.
I'm going for Cambridge, UCL, Warwick, Bath, and Imperial.
UCL sent me a letter on Thursday which said 'based on your application there is no need to interview you; come to London on date X and we'll give you an offer', and just this morning I got a letter from Bath saying 'we anticipate giving you an offer but please come down for a visit and informal interview on date Y'.
No news from Cambridge yet because I've got to send them an additional form which takes hours to fill out, but that should be done by today.
Bath sucks, you should have put Bristol instead.Quote:
I'm going for Cambridge, UCL, Warwick, Bath, and Imperial.
If you get rejected from Cambridge, and then we both get an offer from Warwick and then both get accepted, then see you at Warwick.
I didn't know you wanted to do applied mathematics. Anyway, you should have applied to Oxford, they only get you do a test and a interview, no additional forms. Also, you have to do STEP 2 and 3.Quote:
No news from Cambridge yet because I've got to send them an additional form which takes hours to fill out, but that should be done by today.
I only got an interview for Manchester. I'm surprized you haven't heard anything for Imperial, as in another forum alot of people were getting offers for Imperial.Quote:
UCL sent me a letter on Thursday which said 'based on your application there is no need to interview you; come to London on date X and we'll give you an offer', and just this morning I got a letter from Bath saying 'we anticipate giving you an offer but please come down for a visit and informal interview on date Y'.
P.S. Whats going to be you're second choice? Is it Warwick. As I assume Cambridge is you're first choice.
Bath is pretty good for maths at least; in the top ten. It's my reserve, but seeing as I've got UCL in the bag I guess it's no longer necessary. Pretty place though.
Cambridge has pretty much the best maths course in the world; I didn't ever hear it was better for applied. I mean, considering that it's bred the likes of Andrew Wiles, who solved pretty much the least appliable mathematical puzzle ever. Although saying that, of course I actually do want to go into applied maths, ultimately. Networks would really come into that area; although there is sort of a blurring into pure. Also Cambridge has a reputation for science whereas Oxford has more of a reputation for the arts.
I don't really know what my second choice would be. I heard Warwick has a poor social life and also that they're a little undeserving of their reputation and only require STEP in order to show off and filter off the best students without necessarily providing the best education for them. Then again they do have a variable course which allows you to take 25% of your modules in neuroscience if you want. Same with UCL, they're very variable, and also they are at the forefront of neuroscience research. Imperial's just generally prestigious. All I heard from them so far was a 'thanks for applying', though. They did ask for 80%+ in each module without resits, and I did sort of get 79% on C3 last year before retaking and getting above 90%, but that was a year early so I hardly think they can get fussy about it... I hope.
Number theory is one of the most funded and applied mathematics, i.e. crypotography. Didn't Andrew Wiles say that the only thing different in number theory is that its the most applied subject.Quote:
Cambridge has pretty much the best maths course in the world; I didn't ever hear it was better for applied. I mean, considering that it's bred the likes of Andrew Wiles, who solved pretty much the least appliable mathematical puzzle ever.
Cambridge too me just looks like applied mathematics.
Not really. Comparing Cambridge modules to Oxfords, it seems that Oxford is more pure.Quote:
Networks would really come into that area; although there is sort of a blurring into pure. Also Cambridge has a reputation for science whereas Oxford has more of a reputation for the arts.
Wouldn't it be better to go into mathematical logic, espically since all AI and trying to understand how we think comes into uncertain logic. Well, thats what I heard.
Thats a lie.Quote:
I don't really know what my second choice would be. I heard Warwick has a poor social life and also that they're a little undeserving of their reputation and only require STEP in order to show off and filter off the best students without necessarily providing the best education for them.
Warwick policy of admission I think is really fair. Also, Warwick is known as the third best uni for maths. So I would go for Warwick as second.
I heard they don't like retakes. Maybe this explains why you haven't got an offer from them yet.Quote:
, but that was a year early so I hardly think they can get fussy about it... I hope.
P.S. I would put Warwick as second choice, if you get an offer from Cambridge. Since they are better then all you're other choices.
Some dude that studies math I know said it was mathemathically provable. Then again, what does he know. Then again, who cares. Then again, I hardly ever order 0.9999...99 pancaces in a restaurant.
There have been like a dozen proofs in this thread already. Get your head out of your ass.Quote:
Originally Posted by Neruo
Excuse me? (also: Proof? Where?)Quote:
Originally Posted by drewmandan
Of course I didn't read all the posts in this topics. Also, yeah, probably I didn't really say anything new. Then again, if all the things on the internet had to be new, then this entire topic shouldn't exist.
Also, for practical reasons, anyone that honestly cares in his day-to-day life that 0.999999 = 1 is a faggot.
So lighten up.
0.999999 does not equal 1.Quote:
Originally Posted by Neruo
And you, sir, are the one that is calling people names.
Hey, I fixed your post for ya.Quote:
Originally Posted by Neruo
Regarding your query:
First of all, it is rather obvious that .99... equals 1. Whether or not being intelligent enough to realize that makes a person a faggot is irrelevant.Quote:
Excuse me? (also: Proof? Where?)
Secondly: http://en.wikipedia.org/wiki/0.999... (Make sure you read the first sentence very very carefully).
There have been a couple of valid proofs so far, mine was on the previous page I think.
You have to remember that mathematics isn't 'real', it's a system for shunting symbols about according to very precise rules. Within that system, 0.999... is 1, but bear in mind that neither 0.999... or 1 actually physically exists.
Well, according to same people that know things about maths 0.9999... does equal 1. I am sorry if I confused you by not in fact writing down an infinity of 9's, but shortened it to '0.999999 equals 1'. I see how you got confused there, it's so complicated to see it was an abbreviation.Quote:
Originally Posted by drewmandan
Get your head out of your ass. You can interpret this sentence as me quoting you or as me giving you some advice. Pick whichever you prefer.Quote:
And you, sir, are the one that is calling people names.
-
Thanks, faggot.Quote:
Originally Posted by hungrymanz
Funny how mister intelligent (you) completely disagrees with the person I called a 'faggot'. As far as 'faggot' in the context I used it in was synonymous with 'idiot' or 'ill informed on the subject at hand', I am correct in calling either you or the person you are defending a 'faggot', because of the logic of the excluded 3rd.Quote:
Regarding your query:
First of all, it is rather obvious that .99... equals 1. Whether or not being intelligent enough to realize that makes a person a faggot is irrelevant.
So, I don't know which one of you two is a 'faggot', or 'wrong' if you like that term better, but I am at least certain one of you guys is, and that one should certainly stop pretending to know something about math.
At least I don't pretend to know anything about this kind of mathematics.
Yeah, it read "I am a faggot that uses wikipedia because I know shit about math but like to pretend I do." Really insightful sentence.Quote:
Secondly: http://en.wikipedia.org/wiki/0.999... (Make sure you read the first sentence very very carefully).
I'm going to go ahead and request that this thread be locked. All's there is worth being said on the topic has been said and now it's just being run by a bunch of immature bastards who can't debate their ideas without insulting each other.
:lock:
It's not a matter of debate, since .999... = 1 is provable. You can't debate proofs, especially such trivial ones. Rather, it is a matter of enlightening those who refuse to accept that .9.. = 1Quote:
Originally Posted by Kushna Mufeed
Where the hell could this apply in my life?
Newsflash for Suttsman; you're in the philosophy forum.
Look people, the staff is simply not going to stand for the degeneration of respect towards other members. The over all attitudes from many members have declined considerably. It has resulted in a very negative atmosphere around this Forum.
I don't care what you reasons are.
A continued abuse of this will result in warnings. Eventually and unfortunately member bans.
1/9 = 0.1111111111111111111111111111111...
2/9 = 0.2222222222222222222222222222222...
3/9 = 0.3333333333333333333333333333333...
4/9 = 0.4444444444444444444444444444444...
5/9 = 0.5555555555555555555555555555555...
6/9 = 0.6666666666666666666666666666666...
7/9 = 0.7777777777777777777777777777777...
8/9 = 0.8888888888888888888888888888888...
9/9 = 0.9999999999999999999999999999999... = 1
10/99 = 0.10101010101010101010101010101...
11/99 = 0.11111111111111111111111111111...
12/99 = 0.12121212121212121212121212121212...
That proves everything. :P I guess. Now, finally, we can live together in peace again. :D
I haven't bothered to read the whole thread, I don't know how such a simple question can spawn 7 pages. It is simply a question of can numbers reduce to infinity. And obviously they can (no force but the end of time will stop something from writing out 99999... over and over again), so no it will never ever in infinity time reach 1.
It's a static number, not a process. And by the closure axiom of the reals, it equals 1.Quote:
Originally Posted by LucidDreamGod
WTF? I thought I asked this to be locked? Aren't the staff supposed to lock a thread if the OP requests it?
i've never even thought about this lol.... but I guess I would say they're not equal, since .999 will always be slightly less than 1, and .9999, and .99999 and forever on won't ever be 1.
I'm sorry I didn't get any of that.:?Quote:
Originally Posted by drewmandan
If you don't have the knowledge required to understand statements about the structure of the reals, what makes you qualified to comment on whether 0.9~=1? Anyway, the issue was settled over a hundred years ago.Quote:
Originally Posted by LucidDreamGod
Whether or not it seems that way is irrelevant. .999 repeating 'is' 1. In this context, infinitely close is congruent.Quote:
i've never even thought about this lol.... but I guess I would say they're not equal, since .999 will always be slightly less than 1, and .9999, and .99999 and forever on won't ever be 1.
Example: .3 repeating equals 1/3 right?
and .3 repeating times 3 equals .9 repeating, right?
and 1/3 times three equals one
Therefore one must equal .9 repeating
Maybe, but It seems that 3 * 1/3 is close to 9/9 but not close enough to be exactly the same
What do you mean? 9/9=3/3=3*1/3
This guy is either too young to be here, or he's a dropout.Quote:
Originally Posted by pixies
I went to a uni interview on Wednesday and we talked about some interesting stuff... like how there's the same number of fractions as whole numbers (infinity). But more irrationals (a bigger infinity).
I think .9 repeated does and doesn't equal 1. It really depends on which reasoning you look at it from.
Oh ya
In b4 lock.
From a stand-point that defies all accepted mathematical fact and with reasoning that refuses to pay attention to calculus, yes, I suppose that's right.
It's called countable infinity and uncountable infinity. A set is countable if you can establish a one-to-one correspondence with the naturals.Quote:
Originally Posted by Xei
I know.
So, basically, there is an infinite gradient between numbers and an infinite amount numbers can reach.
Uh.
It could be argued that not even .3 repeated can properly quantify 1/3. Hence the reason why .3 is repeated endlessly, because it can never reach a number close enough to actually be 1/3 of 1.Quote:
Originally Posted by spockman
Since it is accepted in mathematics that .3 repeated does equal 1/3, then yes, .9 repeated does equal 1.
.9 repeated being equal to 1 makes things a whole lot easier.
No, because infinity is not a destination...it's a journey. An endless journey.Quote:
Originally Posted by Kushna Mufeed
Lol, this debate is funny.
.3 isn't 'repeated endlessly' as if it's some kind of process. There exist an infinity of 3s in .3~. If there were a finite number it would be less than 1/3. As there are infinity, it is equal to 1/3.
0.333~ * 10 = 3.33~
3.33~ -0.333~ = 3
0.333~ * 10 -0.333~ = 3
0.333~ * 9 = 3
0.333~ * 3 = 1
0.333~ = 1/3
Only if you factor in time.Quote:
Originally Posted by Black_Eagle
Time??
Saying that infinity is an endless journey implies it is a process which requires time. Infinity is independant of time.
Indeed. Mathematics is independent of time. Certainly number theory.
Let's not get into differential equations... :P
Quote:
Originally Posted by Black_Eagle
Took the worlds out of my mouth :P I thought about posting something similar.
1 can never be cut into 1/3.
And time cannot change that fact.
The derivative of infinity with respect to time?
Uh...yes it can. And you just did it.Quote:
Originally Posted by LucidDreamGod
How did I just do itQuote:
Originally Posted by Kushna Mufeed
.33333....
.33333....
+.33333....
.99999...
1/3
See? I did it again! I divided 1 into exactly 1/3!
______________
3|1.000000000...
Do it.
Am I the only one who gets the feeling that this thread is a debate between college students who have taken advanced math courses and freshmen in highschool?
Nope. :l
Looking at the title I thought you were talking about numbers represented with decimals, and not fractions.Quote:
Originally Posted by Kushna Mufeed
I'm pointing out that the title question is, it will never get to 1.
However I did go into a bit of a problem with 1/3 is not in existence, it is, it just cannot be represented as a decimal, that is what I was meaning to say.
I was also saying that 1/3 is not equal to .3 repeating at least not perfectly. The current decimal system cannot represent that number.