Oh, Math

I have finally figured out why the fact that .999... = 1 bothered me so much. I have it worked out. THIS IS SUCH A RELIEF!!!


I KNOW that there is a number that is infinitely close to zero without actually equally zero, as is demonstrated in the graph of 1/X, just as there is a number that is infinitely far away from zero. In my head I was subtracting 1 - numberinfinitelyclosetozero, which should equal .999 repeating, right? WRONG.

Infinity and a number that is infinitely close but not equal to zero are concepts. Infinity - 1 is still infinity, and you can't do normal math with them and expect normal numbers to come up. .999... is not a number that is infinitely close to one without being one. It is one, because that is how the notation works. There is a number that is infinitely close to one, but is not one, I just don't know how to notate it simply.

ARE YOU HAPPY FOR ME? BE HAPPY FOR ME! I AM A NERD AND THIS PROBLEM WAS DRIVING ME NUTS!

(If you still don't believe this check out wikipedia.)

The way to notate a number that is infinitely close to zero but not actually zero is 1/∞ so if we try and say 1 - 1/∞ we have to rearrange it to say ∞/∞ - 1/∞ or (∞-1)/∞ which can't be solved with normal math. If we were looking for limits we would just say one.

OH MY GOD MY LIFE MAKES SO MUCH MORE SENSE NOW!!!!!