1 = .9999.....

[Luara]

...ah...erm...ugh...


...



you're funny

[Madame Adequate]

How's it going, thread? Been awhile since you rolled around!

[Peegee]

I believe 0.99... doesnt equal 1 but approaches, similar to how the function y=e^x approaches the line y=0 but never touches it.

An expression is not a function. Good try though.

Think about it this way: graph the equation y=0.9999...

It's the same as if you were to graph the equation y = pi - it would be a horizontal line

The expression 0.99999... = 1 is an equality and is also true/valid/whatever

[Rye]

...

[Peegee]

Well what if i worked it out as a series 0.9999... is like y = (1/9)*(10^-n) where n = 0,1,2,3,4,5...

edit:wait let me rewrite that

But it's not a fuction it's an equality.

It's
Not
A
Function

[blackmage_nuke]

I believe 0.99... doesnt equal 1 but approaches, similar to how the function y=e^x approaches the line y=0 but never touches it.

An expression is not a function. Good try though.

Think about it this way: graph the equation y=0.9999...

It's the same as if you were to graph the equation y = pi - it would be a horizontal line

The expression 0.99999... = 1 is an equality and is also true/valid/whatever

I was using it as a comparison not an example

[Madame Adequate]

Listen to peegee, he's azn, he knows.

[blackmage_nuke]

Bah it doesnt matter, the next time this topic comes around my opinion will change again anyway.

[Peegee]

I believe 0.99... doesnt equal 1 but approaches, similar to how the function y=e^x approaches the line y=0 but never touches it.

An expression is not a function. Good try though.

Think about it this way: graph the equation y=0.9999...

It's the same as if you were to graph the equation y = pi - it would be a horizontal line

The expression 0.99999... = 1 is an equality and is also true/valid/whatever

I was using it as a comparison not an example

[q]Listen to peegee, he's azn, he knows. [/q]

Well no, I'm quite terrible at math, but if you looked up old eoff threads about this I used to think 0.999... was akin to a function that was as close to 1 as you could get.

Now in practice no number is 'the smallest', as you can always divide it by another real number, thus getting a smaller number.

The expression x = y is just that - an expression. When you see x you sub in y.

So in the example x = 0.999... all you get to do with it is sub 0.999... into x. Since there's no associated function (like y = x^2) there's nothing more you can do with it.

It's I dunno, number theory.

[Madame Adequate]

I dunno how good you are at math, but I know you're right about this.

[blackmage_nuke]

The real question we are asking is does 1/infinity truly equal to zero? becaus 0.999... is really 1 - 1/infinity

[Unbreakable Will]

ow...
my head hurts...

[Peegee]

The real question we are asking is does 1/infinity truly equal to zero? becaus 0.999... is really 1 - 1/infinity

Infinity is not a finite, real number.

[q] I dunno how good you are at math, but I know you're right about this.[/q]

I was reading a pre-calculus notebook yesterday. Though formally I've gone about as far as integrals before my brain hurt very much.

[blackmage_nuke]

The real question we are asking is does 1/infinity truly equal to zero? becaus 0.999... is really 1 - 1/infinity

Infinity is not a finite, real number.

Yet we constantly use it in other proofs

And no amount of evidence or reasoning will make me see that the infinitely small difference between 0.999... and 1 does not exist

[Rodarian]

... I sucked at Math....