Thread: Analysis

By constructing an appropriate one-to-one, onto function, prove and C= U {-, } have the same cardinality.

Originally Posted by boardinfanatic89

By constructing an appropriate one-to-one, onto function, prove and C= U {-, } have the same cardinality.

Let f(0) = -infinity, f(1) = infinity, f(n) = n - 2 for each positive integer n > 1. Let f(x) = x for all other x. Then f bijects R onto C.

Would it be possible to remove f(n) = n - 2 for each positive integer n > 1 and just have f(x)=x for all x in R?

oh nevermind, you need it so that it covers values 0 and 1. Got it, thanks.