evasive wrote:

like this. there's some light coming from the farthest star and travelling billions of lightyears. you take a bit of the thinnest black paper. compare the distances. the final distance will not be zero. not ever. you will never reach the surface. so, 0.999999....... is not 1. done.

Don't really know what you are trying to say there. Light traveling to and from somewhere has a fixed distance. Also, a thing piece of black paper has a fixed thickness. Not sure where that came from though. What distances are you comparing? And what "surface" are you trying to reach?

Roach412 wrote:

that is exactly what i'm saying, and holds true in all math. each number is unique, even if it is the same value. 1 has the value of 1, but it is not the same as 1, it's like clones. they are different...else you cannot do a comparison - which is just plain logical reasoning.

Why would the same numbers need to be unique? Can't say I've heard of that reasoning with numbers. Two of the same numbers are just that, the same, not unique.

Edit: Another point using a more logical approach would be that, if two numbers are in fact different, then by definition there HAS to be a number between them. What number is between 0.999... and 1? There isn't one. Instead of trying to think what it would take to "get to" 1, what would it take to "move away" from 1? Any number you think of will be 1 too many and move you BEFORE 0.999...

Mentally, the only way you can say that 0.999... is smaller than 1 is if you stop repeating the 9's in your head. When in fact they don't ever stop. In order for it to be smaller than 1, the 9's have to stop. So the number will never be smaller than 1.