0.999....=1

[JRPGfan]

Teeqoz said:

JRPGfan said:

For some reason I dont like it...

Because your still missing that 0.000000000..... 01 if you go infinity far out to reach it.
But I can understand in the practical world, 0.99999 ect = 1.

There wouldnt ever be a practical time, where 0.999 infinity far out, wasnt ever the same as 1.
Because our real world doesnt work that way, theres nothing infinite in it.

 

This is like when you divide by infinity, and which side of numbers you come from... its weird stuff :p

You are thinking of it as more like a very long but finite list of 9s.

0.000...1 wouldn't work.  You can't have an infinite number of zeroes followed by a 1, because the zeroes go on forever, there is no end, so there will never be a zero after which you can place the 1. It's like saying "There's a 1 in the infiniteth decimal place". That decimal place doesn't exist, because if it did, it would have been finite.

The same is true for 0.999999999 though.

Why do you have it work for one thing but not another?

The proof looks solid enough though, the concept itself is what I have a hard time wrapping my mind around.

 

Note Im not saying that 0 is the same as 0.0000000 ect 1.

Im saying that 0.99999999 will always be missing that 0.00000000 ect 1 part, that keeps it from being a pure 1.