- If $m+n = m+k$, then $n=k$.
- If $mk = nk$ and $k\neq0$, then $m=n$.
I'm not sure what t do. Do I have to use math induction or not? (Base on Peano system)
2026-03-28 15:19:38.1774711178
How to prove these problems? (Operation on N)
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If you want to prove these sort of things in Peano, then using induction is probably a strong candidate for the first attempt.
To prove the on about addition, use induction on $m$. Note that this requires you to know that $x+y=y+x$ first, which you can also prove using induction. Similarly, the multiplication should be proved by induction on $k$.