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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
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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?