[Polpolion]

Is 0.999999999 (repeating) equal to 1?

I've noticed that 1/9=.1(repeat), 2/9=0.2(repeat),...8/9=0.8(repeat), so wouldn't the next logical step be 0.9(repeat), but 9/9 is one.

[tinfoil]

that one's always confused the **** outta me. anyone clarify for the both of us?

[CP5670]

This has to be one of the most common math questions on forums.

Yes, they are the same number, one that happens to have two decimal representations. There are a couple of different ways to see this, using decimal shifts or limits.

[tinfoil]

so it is 1 then

[General Battuta]

Yep.

[tinfoil]

that's silly

[portej05]

Interesting question... the answer is certainly counter-intuitive

Think of it as the limit of the difference between 1 and 0.999...
For any given number of decimal places (n), the difference is 1/(10^n). The limit of that is 0 as n tends to infinity.

[Dark Hunter]

Here's another:
Any finite number divided into infinity parts comes out to be zero.

But zero multiplied by infinity is still zero.

Interesting, eh?

[CP5670]

But zero multiplied by infinity is still zero.

Not necessarily. It's an indeterminate quantity that can be anything, depending on how "strong" the zero and infinity are.

[Mars]

I think I'll stick to College Algebra. I'm really hoping Journalism never sees me having to know what the hell you just said.

[Nuke]

those 1s and 0s are really just a difference of signal voltages in the hardware, and the bool operation is depending on your relation to a particular threshold. over it is one, under its zero. because there are fluctuations that occurs in the electronics as paths open and close changing the power requirements. oh and im high

[Bobboau]

depends on who you ask mostly, most mathematicians say yes, I say no, my position is one mostly of semantics, as I believe the other position is as well.

[Flipside]

I'm with Bobboau here, mathematically speaking, it's one, but you only have to look at the two numbers to see there is a difference, it might purely be a conceptual one, due to the nature of infinity, but a difference is there in my opinion.

[ssmit132]

I'm with the 1 = 0.999... part, because, IMO, it makes sense, also it's the only way 1/3 = 0.333... works when 3/3 = 1.

1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.999...
But 3/3 = 1
Therefore 0.999... = 1

There is no definite difference between 1 and 0.999..., therefore it's an infinite difference.

[Flipside]

But is infinite difference the same as no difference whatsoever? We all know that 1/3 = 0.3333333etc is an estimate, that the true answer is infinite in size, we can get the answer to any sum up to any resolution if we have the tools to calculate with it.

However 1/3 is a symbol, like Pi or 6.02x10²³ - They are not numbers, they simply represent much longer numbers. You could say the same about 0.999999999, it can be represented as '1' but in truth 1 is only a symbol to represent a number too large to be written.

[ssmit132]

But is infinite difference the same as no difference whatsoever? We all know that 1/3 = 0.3333333etc is an estimate, that the true answer is infinite in size, we can get the answer to any sum up to any resolution if we have the tools to calculate with it.

That is what I meant.

However 1/3 is a symbol, like Pi or 6.02x10²³ - They are not numbers, they simply represent much longer numbers. You could say the same about 0.999999999, it can be represented as '1' but in truth 1 is only a symbol to represent a number too large to be written.

Yes, but 1 is also an integer. Numbers are usually used as representations of transcendentals when they come from numbers, aren't they? Like the square root of two - √2 is an exact value, but 1.4142135623730950488016887242097 is an approximation. Therefore, it is possible that 1 is an exact value and 0.999... is an approximation.

[pedantic] And it should be written as 0.999... , as 0.999999999 is also an exact value. Even though we know what you mean. [/pedantic]

[Flipside]

Actually, I thought about using the three dots and thought 'Oh, they'll know what I mean'

Now you mentioned it, there is actually one tangible difference between the two. and that is that the integer 1 is part of a set of integers, whereas the value 0.999... is not.

[Col. Fishguts]

X     = 0.999...       / multiply by 10
10X = 9.999...       / -X (and since X = 0.999...)
9X   = 9                /divide by 9
X     = 1
==========

-> QED

Of course this relies on assumption that you can agree that 9.999... - 0.999... = 9
So it's still semantics, but it demonstrates nicely that the obfuscation is in your head, and not in math.

BTW: If you really want to stirr up some serious forum drama about math/physics, start a discussion about the the goddamn airplane on the goddamn treadmill

[ssmit132]

Have you seen Mythbusters? That myth has been disproved. The plane will take off because the propeller/jet, not the wheels, are providing the propulsive force.

Do not let this devolve into flame war, otherwise I will be ostracized. (Don't really know what that means... I shouldn't put that, it might mean something evil...)

[Flipside]

LOL It'll be Slide Rules at Dawn