I need some help on homework. Here is the problem I am stuck on:
Prove that every closed interval [a,b] is numerically equivalent to [0,1]
I believe that I need to find an injection between the two sets. But I'm not sure how to get there. Any help would be great! Thanks
Look for a function $f$ of the shape $f(x)=kx+l$. Your conditions will determine $k$ and $l$. It is simplest to go from $[0,1]$ to $[a,b]$. So we want $l=a$ and $k+l=b$.