Tell me more ×  Let $[n]$ denote $\{1,2,\dots n\}$.  Show there
is a bijection between $[m]\times[n]$ and $[mn]$.  I was
thinking about doing something related to induction to prove
that there is some value $b$ for every $f(a)$. Then probably
settle for the definition of a product to say that in
$\{(a,b)\mid a\in A ; b\in B\}$ so there can only be values
corresponding from $A$ and $B$ in $(a,b)$. If this seems
correct, let me know.  If there's anyone with a more rigorous
proof, I would be delighted.  share|improve this question The
first step would be a more rigorous statement of what you're
actually trying to prove. e.g. what function from what domain to
what codomain are you trying to prove is bijective? –  Hurkyl
Sep 14 '12 at 12:27 Guessing: are you finding a bijection
between $[m]\times[n]$ and $[mn]$? –  rschwieb Sep 14 '12 at
12:30 Apparently, this question is about showing $|A\times B| =
|A|\cdot|B|$ in the finite case. –  Hagen von Eitzen Sep 14 '12
at 12:30 @rschwieb Yes, I just seem to be inefficie