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Jul26-11, 01:21 PM
P: 460
Quote Quote by micromass View Post
We use technical terms because mathematics is technical. Mathematics uses very precise statements, and I feel that I am lying if I do not use these statements.
You can always ask for more explanations if you don't understand something, but eventually it will be up to you to learn these precise statements.
One cannot do mathematics while using handwaving arguments.

Fair enough,

[tex]\mathbb{R}\rightarrow ]-a,a[:x\rightarrow \frac{2a}{\pi} atan (x)[/tex]

is a bijection between the reals and an interval ]-a,a[. So any open interval can be put in one-to-one correspondance with the reals in this manner.
Can you post a picture of the bijection, my browser does not decode TeX