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In a paper I'm writing (purely recreationally, nothing fancy), I state that "an odd number minus an odd number = an even number". I also state that "an even number minus an odd number = an odd number".

Now, should I provide the proof for this in the last section of my paper? And if so, is there a standard proof?

I was thinking Euclid's proof, but perhaps there is a standard proof for every principle or axiom (or whatever one would call it). Maybe Euclid's proof is the standard?

A. Kvåle
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  • This really depends on what you are assuming in your writing. A case could be made that both claims are too trivial to bother with proving, as $(2n-1)-(2m-1)=2\times (n-m)$ for example. But perhaps you are not assuming that odd numbers are those of the form $2n-1$. – lulu Oct 17 '20 at 13:18
  • In a reserach paper, one would not even mention the general principles that odd number plus even number is odd, et cetera. If there is some interest in showing that $A+B$ is even/odd, and for some reason the parities of $A$ and $B$ are hard to evaluate, one would just prove that $A$ has the appropriate parity and $B$ has the appropriate parity, perhaps prefacing it with "We'll prove that $A$ is [odd/even] and $B$ is [odd/even]". –  Oct 17 '20 at 13:19

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