If you're having math problems, I feel bad for you, son...

[napoleon_in_rags]

9. I will make it simpler for you.

My point is that integers of infinite length aren't allowed, and we should look at why. For instance, in the video, she says that for any given integer n, there is a larger integer n+1. But lets suppose instead, my integer is defined as

m = 1+1+1+... (to infinity)

can you add 1 to this infinitely long integer and make it larger? Its value is already infinite. Can you get a larger number with infinity plus 1? No.

Now consider the real number line. between any two numbers A and B with A < B, there are infinite more real numbers in the interval between them. And furthermore, I can choose a new number C which is 9/10ths of the way between A and B, but still less than B. So for example, if A = 0 and B = 1, I can choose the point C = 0.9 which satisfies that condition. And looking at the new interval between 0.9 and 1, I can choose a new point, 0.99 which is 9/10ths of the way between those. And yet another point between those, 0.999. Generally, I realize, that I can just stick another '9' on the end of the decimal to attain the decimal representation of the next number which satisfies that condition starting at 0 and 1. But what about the number 0.999... (repeating) can I stick another '9' on the end of it to find the next point? No. Just like I can't add 1 or 1+1+1... repeating to get a larger number. So does the common sense idea of there always being an interval between two non-equal points really make sense for this kind of number? No.

The point is that the rules change when you get to this numbers with an infinite expression, like 1+1+1... or 0.999... Specifically, they are ill defined. For a person who believes 1/3 = 0.333... of course .999 repeating equals 1. But why didn't you just say 3*1/3 in the first place?