Thread: Does 0.9 repeated = 1?

Originally Posted by xXSomeGuyXx

I also have three 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
For dem algebraic freeks out there:
.999x = 1
x = ...? I dunno. BECAUSE 1 AND .9999999999999~ ARE NOT EQUAL NUMBERS.

2. Now get rid of the decimal.


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.

Originally Posted by A Roxxor

2. Now get rid of the decimal.


4.

You fail at algebra.

.999...x = 1

x = 1/.999...

x = 1

Again, x = .9...; 10x = 9.9...; 9x = 9; x = 1

In case you haven't noticed, that post was edited...

And I don't fail at algebra.


@ Xei, what's wrong with the Density Property reason?

2. Now get rid of the decimal.


4.

You fail at algebra.

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.

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.

Originally Posted by xXSomeGuyXx

In case you haven't noticed, that post was edited...

And I don't fail at algebra.

Well, your first last proof didn't make any sense

And y = .999... is the same as y = 1. Because .999... = 1.

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.

Then what is the fractional equivalent of .999...?

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....

9/9 is .999... and, unless you're mathematically challenged, equal to 1.

Originally Posted by arby

The big problem I have with these proofs is that you are applying rules meant for rational numbers on irrational ones.

.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.

Besides, by your logic 5 is an irrational number. Since 5 = 5.000....

And I don't fail at algebra.

You do:

.999~ + .111~ =1

Originally Posted by Omnius Deus

Hungrymanz, you just NEED it to be 1 so the universe can exist in a logical, fluid way.

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.

It [the universe] doesn't [exist in a logical way].

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.

I, and several others, have proved that .99... equals 1. As yet there have been no correct proofs to the contrary.

Originally Posted by A Roxxor

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 like saying that 2 != 6/3 because, actually, it's 4/2.

7. .999~ doesn't even look like 1!

Are you trolling?

10 doesn't look like 1+2+3+4.

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?

You're not a mathematician. A few of the people here are.

It can be written as 1/1.

Originally Posted by xXSomeGuyXx

Lol, we've been at this for pages!

7. .999~ doesn't even look like 1!

5*1 + 3*2 - 3*3 != 2

by your own logic.

Originally Posted by Xei

I've never heard of density property and Wikipedia has nothing to say about it.

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:

http://en.wikipedia.org/wiki/0.999#Analytic

Originally Posted by xXSomeGuyXx

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.

Who said 0.9~ = 0? I don't remember saying that.

Originally Posted by arby

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?

Rational numbers are numbers that, in decimal form, either repeat in a pattern or terminate. 0.999... is rational.

9/9 is .999... and, unless you're mathematically challenged, equal to 1.

Exactly

If only we had 6 fingers on each hand instead of 5, and had a mathematical system based on the number 12.

Originally Posted by hungrymanz

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.

I'll sit here untill I do.

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....

9/9 is .999... and, unless you're mathematically challenged, equal to 1.

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~.


.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.

Who said it wasn't? Really?
Besides, by your logic 5 is an irrational number. Since 5 = 5.000....


You do:
That isn't even close to algebra. That is a numerical expression, not an algebraic expression. ERGO, I do not suck a algebra. Test me. Give me a loong ass algebraic equation and I'll find x for ya.


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.

Oh, because that REALLY makes sense. God exists because he does.

Mine are in bold.

Rational numbers are numbers that, in decimal form, either repeat in a pattern or terminate. 0.999... is rational.

No. They are fractions of whole numbers.

0.999~ doesn't terminate.

I wish you'd terminate.

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~.

SomeGuy you are deliberately trolling.
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...

Oh, because that REALLY makes sense. God exists because he does.

I proved .999... = 1 whereas God has not been proved.

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!