Does 0.999... equal 1?

Right, so there is no "last number" or actual infinity.

 

There is no last number because the numbers extend forever. Infinity is not a place you can reach.

 

So you cannot multiply infinity by anything.

 

because it yields infinity it is still unreachable

 

The thing is, however, you cannot perform mathematical operations on anything but an actual number

 

.999 = .999 not 1

 

Your technically right but there are certain times which might need to. Could you tell me what that has to do with your argument.

 

That is only true because in the "basic" math you probably do, you round off numbers somewhere. If, as is the case in this question, you were to extend to infinity, the number would equal one. Lol, I admit it, this question intrigued me enough that I went and asked my calculus teacher and he said that yes 0.999 to infinity does equal one so unless you teach calculus - HA!

EDIT: Sorry I saw this and had to comment

Um that isn't the question. .999 is way different from 0.999... to infinity. Sorry but unless you have gaduated 1st grade don't comment

 

There are no times that you need to.

Earlier, you were, as part of your argument, trying to establish that infinity / 2 = infinity.

Dusk, mathematics is base upon rules of logic. If a conclusion can be reached using algebra, then it can be reached using calculus, or any other form of math.

Refute this: 0.99 repeating is NOT equal to 1 because at no point in time will you add a 9 and be able to say "Oh, look, it's equal to 1 now!".

 

okay, in human not mod language (lol) you'd never get 1 with 0.999

 

infinity/2 is still infinity.

That's how it behaves. It's not a number, it's a concept... or a behavior.

Shredder, I'm not sure which side you're on now - but you since you agree that a conclusion reached by algebra is valid in any other field of mathematics, the algebraic proof stands.

.9... = 1

 

A point in time is finite. you would need to go PAST time in order for it to reach 1 and that is what we are doing here. We are going to infinity.



There is an infinite ammount of numbers between 0 and 1.

There is an infinite ammount of numbers between 0 and .5.

the limit of x/2 as x approaches infinity is infinity

 

I would say yes if there are never ending 9's.

 

The algebraic proof is not valid. If you think about it as simply as you can, there is no point at which you can add a 9 and magically turn the number into 1.

You also cannot really divide concepts by two.

So, after how many 9's will it equal 1?

 

Maybe its to abstract for you. We are not going to a finite point. We would have to go to infinity to get to 1 which is what .999... means.

 

I can understand the concept, yet I reject it.

At .9, the difference is .1. At .99, the difference is .01. At .999, the difference is .001. So, if you extend it into infinity, the difference becomes infinitely small.

 

I posted this on offical forums ages ago but it died.
This is how i learned it.

X = 0.111111
10X = 1.111111

so, 9X would be 1.
Divide them out and it's 1/9

So, carrying on.
0.9999 is 9/9 which is 1/1, which is 1.

 

0 is infinitely small.

Any two real numbers have a real number between them unless they are the same. Name ONE real number between .999... and 1.

 

No, if x = 0.111...111, then 10x = 1.111...110.

Incorrect. Zero is nothing at all. 0.000...001 is infinitely small.

It's impossible, since there are infinite 9's. The concept that there is always a number in between relies on the two numbers not being infinitely specific.

 

As Shredderbeam has already said, as well as countless other people, it is an infinitely small number, but a number none the less.

I'll add more in a minute once I get a trade out of the way.

EDIT:

If .999... is equal to 1.

Then .989... is equal to .999.

If that's true, then .979... is equal to .989....

And so on. Your logic is flawed, as is math. I said it before, and I'll say it again. Give me 3 equal numbers in decimal form that add up to 10. IT IS IMPOSSIBLE.

NOT ALL VALUES CAN BE REPRESENTED EAXACTLY in decimal form. The decimal system works in bases or powers of 10. Things like 1/3 or 2/3 CANNOT be represented in decimal form.

FRACTIONS ARE DIFFERENT then decimals, some of you don't seem to grasp that concept very well.