yes

This post was edited by J_B on May 18 2010 09:29pm

Try it with a calculator.

Notice how the more decimal places you use, the closer to 1 you get.
For example, .1*7 = .7,
.14*7 = .98 (ahh much closer),
.142*7 = .994, etc etc.
The only way it would equal *exactly* 1 is if you could take .142857142857.... (repeating infinitely) and multiply it by 7. However it is technically impossible to use a calculator to do such a thing, since we cannot actually type out the decimal form of 1/7 since it goes on forever.

But to answer your question more simply, of course it equals 1: .142857... and 1/7 are *the same number* so they behave in exactly the same manner under arithmetic.

Just that 1/7 makes it a lot quicker than to write it down the other way?

Yes it does. .999999.... going to infinity gets so infinately close to one that it is, for all purposes, one. I could post some proofs but honestly, I dun fee like it lol

not quite
it's not arbitrarily close to 1
it is one

Sure, you can think of it like that. But there's more to it than just that. There's a matter of precision. If you're working on a problem and you come across the quantity 1/2, you can surely write it as 0.5 - not just because it's short/easy to write down, but also because there's no confusion about what you're talking about. 1/2 is 0.5. ANY decimal representation that you write down of 1/7 will be an estimation: 0.1428 is very close to 1/7, but they aren't the same. So if you want to be precise, use 1/7.



There's no such thing as "infinitely close" in the real numbers (this is a consequence of the Archimedean property). So no, .999... is not infinitely close to 1. It IS one.

No.
.9 bar will always be one fraction from a whole

Let's put it this way.
You have a cake.
Someone asks for 0.999... of the cake.
No matter how much you cut off, regardless of how small it is, you would have cut off too much.
The only way to cut off exactly the right amount would be to cut off nothing at all.
Also, if someone asks for 0.000... 1 of a cake, then no matter how much you give him you would have given him too much.
The only way to give 0.000... 1 of a cake is to give nothing at all.
Therefore 0.999... = 1 and 0.000... 1 = 0, so those of you who are saying that you have to add 0.000... 1 to 0.999... to make 1, you are really just adding 0 to 1 which does nothing.

Oh crab.

But this must live.

You're right about 0.999... = 1, but 0.000...1 is not a real number. It is not equal to zero.

This thread will fucking THRIVE as long as retards keep posting...because angry math nerds like myself will continue to tell them they are retarded.