Q: Show that any two intervals (a,b) and (c,d) have the same cardinality
So I guess I have to show there's a bijective function?
So f: (a,b) --> (c,d)
and f(a) = c
f(b) = d
In general f(x) = sx + t, just using different letters
So f(a) = sa + t = c
and f(b) = sb + t = d
Subtracting the two (sa + t) - (sb + t) = c - d
s(a-b) = c-d
Am I going along the right lines for the proof? How would I write out the final function and prove it's a bijection?