Sorry folks but he's right.  0.999... = 1.  Please do challenge and think about it for as long as it takes you, as this part of number theory is important, but be assured, if your challenges and thoughts lead you to think they aren't equal, you've done something wrong.

"but there are numbers between 0.999999... and 1"

The reason why some people doubt this equality is because they naturally assume that the decimals must end at some point, since after all it's much more intuitive for us to assume that everything has an end.

Thanks a lot! That was pretty cool, and it cleared my head of some very tedious questions.

0.999... ≠ 1  Yes, the 9s go on forever;  I am not assuming that they stop.

Amazing how such a concept can completely fly over the heads of so many.

It's the mathematical version of "why?"

here comes the infinitness in play. you have an infinity number of zeros before this 1. so you'll never come to this one and so it's equal zero.

You're so smart.

No, you can't because atom space is not continuous, you can't say it with natural numbers either. 7 and 8 are different but there is nothing between them in natural number space.

That's actually a really great way of explaining it!

How about writing in this way:

This is the way I want mathematicians to tactle the topic 'algebraic and geometric' sequences.Who is willing to bell the cat.

nice! im just waiting for something on this topic to pop up so i can be like "no! your wrong..."

Well, if you introduce some other space then you can say whatever. But I don't think here we were out of real space.

Thank you for posting this as if nothing else it was thought provoking which I can not say for 99.99999999%repeating of Youtube vids =P

Fun with the concept of infinity.