Re: Cantor and the binary tree



mueckenh@xxxxxxxxxxxxxxxxx wrote:
> Is here a bijection possible between uncountable sets?

Sometimes.

There exist bijections between R and C, for instance. But
not between R and P(R).

> Can you enumerate R <--> R?

I can construct a bijection from R to R, if that is what
you are asking.

Here's one: f(x) = x.
Here are some more:

f(x) = x^2 if x>=0, -x^2 if x<0.

f(x) = x^3

f(x) = 1/x if x != 0, 0 if x=0


- Randy

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