I agree, and on strong mathematical bases.

First proof:
1 = 3 * (1/3) = 3 * 0.333333... = 0.999999...

Second proof:
When dealing with real numbers in the set R, the following holds:
Given a, b € R such that a < b, there exists c such that a < c < b. A trivial example is always (a+b)/2, i.e., their mean, which is equal to a only if a = b.

Then, take a = 0.99999... and b = 1, and suppose a < b. Then there must exist a < c < b for some c. Which is that number?
There is none, hence a contradiction. By this contradiction, we know that it is false that a < b. Hence a = b.

For better constructed proofs, I suggest you read:
http://fr.wikipedia.org/wiki/0.999...

"0.999... is exactly the same number as 1. It is just another way of writing it, much like 2-1 or 3/3."
so 2-1 is a number too? i think you're being loose with your definitions. one of my teachers drew a circle on the board and said it wasn't a circle... but it sounded like bs to me tbh. if you have two "numbers" and can't even tell if they are the same number or not, then you need another word other than number to call them. i would not call 0.99... a number, i would call it an infinite sum. and i would not call 2-1 a number i would call it.... something else. an expression or something.

Well, you'd be wrong, bolshoi. I'm not being loose with my definitions at all. The following is true:

2 - 1 = 1.

The right hand side is certainly a number, and the "=" sign means that both sides are precisely the same thing, so the left hand side is the same number.

"if you have two "numbers" and can't even tell if they are the same number or not, then you need another word other than number to call them."

Why? If there are a bunch of people in a room and I'm not sure how many, that doesn't mean that there isn't SOME number that's equal to the number of people in the room. I don't have to know the value of a number for it to be a number.

I feel a Diplomat32.9999... coming up trolling the forum with math puzzles

@zultar what the hell is your problem you pathetic little twat? I've seen several pretty tasteless comments from you to taos and to Sebass and they annoy me. Seriously.

Can we just wrap this up by saying that 0.9999... recurring = 1, the proof has even been given to show that this is the case, and if you don't agree, you're a complete idiot who can't understand simple mathematical concepts? Seriously, is the education system so shit that I have to put up with so many retards insisting that 0.9999... =/= 1, even when substantial evidence has been given to prove that they are equal, because it's fact, and the only evidence against is: "hurr durr, it's a decimal so it must be smaller"

This thread reminds me of the idiots who believe a negative multiplied by a negative is not positive.... Doesn't matter what evidence you show them, stubborn retards cannot learn, as they cannot accept they made a mistake.

the "=" sign means that both sides are precisely the same thing

that's not what an equal sign means. you're thinking of a triple bar sign.

0.9999999 x 100 = (100 lots of 0.99999999) = 99.999999999
Subtract (1 x 0.999999) = (99 lots of 0.999999999) = 99
Divided by 99 = (1 lot of 0.999999999) = 1.

"that's not what an equal sign means. you're thinking of a triple bar sign."

No I'm not. I'm familiar with both. I meant what I said.

@bolshoi, "one of my teachers drew a circle on the board and said it wasn't a circle"

HOLY COW

What sick institution was that? The Soviet Orphanage for Children of Deported Rebels???

lol@rh.

He might have meant that it wasn't a PERFECT circle, which is true.

That has nothing to do with numbers, though.

Nonono semck83, this is not the thread to be sloppy and forget adjectives, he said "it wasn't a circle". Saying that that is the same as them having said "it wasn't a PERFECT circle" is just the same as... I dunno... saying something completely moronic like .9999... being the same as 1 or something...

I think what we have here is adults with a heavy math background (if not flat out math major) and younger kids still in high school.

sjrd basically gave you a pseudo proof by induction. If you gave your teacher his reply, your teacher would agree 100% with it.

Math is a tricky thing. You want to listen to people like sjrd and semck83 and question how things work more than argue. These guys are definitely telling you truth and are very knowledgeable in what they are saying (I'm an engineer with a math minor that graduated college over a decade ago).

I'd also like to mention that sjrd's link is the french version of wikipedia, so just change the 'fr.' in the beginning of the link to the shorthand of your native language, or remove it for english ("http://wikipedia.org/wiki/0.999...").

@bolshoi: It's funny watching theatre majors try to do the maths.

I gave out so many +1's on this thread it isn't even funny.

On one side: mathematicians/scientists.
On the other: people who believe irrational numbers are fake because they are "irrational."

Yes, same number. In the same way 1/3 and 0.3333... are the same number.

@Yj Let's talk about trancedental numbers then!

I can't believe we're actually arguing about this. It can be proven (and has already been done in this thread) that 0.9999999... = 1, using very simple algebra that cannot be refuted. Why do we have all these people in denial about it? You don't get an opinion in math. Math does with statements that are empirically true or empirically false, and never mind what you "believe".

I am so disappointed by some of you.

Transcendental*

@yellowjacket: "On one side: mathematicians/scientists."

Hey now... I know Abge is more on the scientist side, but I'm an engineer. It's about application for me. But I do love me some maths (as do all engineers).

no thanks sqrg, I don't think religion has any place in math.

2 + 2 = 5!

Why?

That is the way God intended it!

@sgrg: "Let's talk about trancedental numbers then!"

Heh... you trying to confuse the already confused kids on here? Confuse them enough to throw their hands up and yell "FINE!" and walk off in a huff?? ;)

http://f.images.memegenerator.net/instances/400x/15152861.jpg

Ok, now we are getting into goodies that are going to end up in my profile! :D

naww FK see above... I include engineers as scientists. They are like scientists who want jobs.

lol honored to see I made your wall of fame, FK.

WHAT IS MATH

WHAT ARE NUMBERS

http://www.youtube.com/watch?v=K5G1FmU-ldg

Eh, trancendental numbers are easy. Let's discuss quaternions.