Proof

[Reach]

Originally Posted by spyke252

I thought saying .9 repeating was understood to mean
_
.9, which is a decimal with an infinite number of nines behind it. It seems like common sense to me, as you can't measure how fast a nine is behind a decimal.

It seems easier to just say 1.

But yea, I suppose if by repeating you are assuming the repetition exists infinitely, then it's correct, for sure.

I just remember losing points on a test once for writing a repeating decimal like that instead of the fractional value...XD



Infinity isn't a number, but it's certainly a concept. And conceptually, if there are an infinite number of 9's behind a decimal than you have one. It's kind of hard to imagine because nothing that represents infinity actually exists.

For example, if you were to try to imagine an infinite velocity you would start getting quite confused. Imagine that. It would require an infinite acceleration. How would you even go about moving in that case? Would you not move or simply exist everywhere that exists all at once? ;o (or well, for the sake of calculus you can just write DNE ^_^).



The same goes for trying to say you have 'infinite something' . It would be impossible to prove there is infinite anything because it exists everywhere that can exist at any given time, therefore it would be impossible to ever prove it true as finite beings.

And then you have the paradox of something infinitely small not existing at all.

anyway