Quote Originally Posted by yasunobu13
Then why don't you believe math teachers when they say it does?
because he's wrong, don't twist it! he didn't prove anything! he just didn't!

I can prove he's wrong, it's just that you don't fully understand the concept of infinity so there's no point for me to even try.

however,I have an idea and I will try
this will not prove anything, but it will show you the whole thing from the different angle

ok, here goes:

draw a line. let's say that the length of this line is 1. now, let's split this line in 2. you'll have 2 sections each is 0.5. now, take any section and split it in 2 - we have 3 sections: 0.5, 0.25 and 0.25. Now take the last section and split it in two, you'll have 0.5, 0.25, 0.125 and 0.125. now split the last section in 2... and so on. You can go on like this forever, you can always split a section in 2, no matter how small it is.

now, you have an infinity of numbers, but if you sum all of them, you'll always have 1 (is anything ringing at this point?)

ok, now understand this - when you sum those numbers going from left to right (0.5 + 0.25 + 0.125 + ...) your final number will get closer and closer to 1 (0.999...), but will never reach it, unless you'll add all sections. the last section (that does not really exists, since you're always spliting) is 0.000... ...001 big

"Infinite" does not mean it "has no end" (and at th same time it does). You have infinite numbers, but if you sum them - they'll give you 1 It's like i (-1^1/2), it doesn't really exists, but it is.

I hope this helped just a little bit...