I was checking for counter examples and then I understood why this was upvoted
this post was submitted on 12 Nov 2023
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Quick Proof: Let k be an even number, then (k +1) is odd.
(k +1) + (k+1) = k + 1 + k + 1 = 2k + 2 which will be even.
That's if you add two of the same odd number. The more general proof is basically the same though: let n and m be integers, then 2n+1 and 2m+1 are odd. (2n+1) + (2m+1) = 2n + 2m + 2 = 2(n+m+1) which will be even.
This is why I failed at uni. I'm struggling so hard to make sense of such proofs, even if I understand the underlying concepts.. :(
It helped me to lean on the different principals as an example.
The easiest being Principal of Induction. Substitute m and n with 1,3,5,7,9...
After going through a few iterations you can see if it holds up enough to keep testing with other principals. (Super simplified).
Or you can just like, understand that an odd number is one more than an even number so if you add them together it's two more than an even number, hence even.
Definitely, that's how I'd explain it in words
Meow
Addition is science.
Always has been