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The question also states that we dont have division and we have not proven any cancellation law, nor do we have 0.

I thought of proving this by induction:

Base Case: $n=1$. $b$ x $1$ = $c$ x $1$ implies $ b = c$

I am stuck on how to do the induction part?

theshah
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  • Are you familiar with the Peano axioms, and in particular with the recursive definition of multiplication? – 79037662 Sep 27 '19 at 17:50
  • If so, see here: https://math.stackexchange.com/questions/2875553/multiplication-cancellation-property-by-peano-axioms – 79037662 Sep 27 '19 at 17:51
  • https://math.stackexchange.com/q/3365019 , are you asking part c) of this question? – Ethan Sep 27 '19 at 20:11
  • Please use the body of the Question (not the title only) to give a self-contained presentation of the problem you want help with. Here the mention of what you are not allowed to use invites guesswork for Readers as to what is allowed. – hardmath Sep 28 '19 at 16:56

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