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lately i have been reading in maths a lot and started to look more deeply into 'proof'. however, i have come across a few proofs that seem a little 'silly'. for example, taking to an extreme, the extremely long proof (many hundred of pages) for 1 + 1 = 2. now i havn't actually read this proof, but I rekon i could reason it quite simply (probably my lack of experience and nievity saying this haha). anyways, here goes:

1 more than something, is one integer more than something. so, using the arithemetic counting (1, 2, 3, etc...), surely it is easily to see that the way to prove 1 + 1 = 2 is: start at 1, and count 1 number higher (adding 1 is moving one up the number line), therefore, 1 + 1 = 2.

now, i think my proof may not be rigorous because maybe I am assuming that "adding 1 is moving one up the number line", but surely using axiomatics (is that a word?) and going further back is unnecesary, because then you also get into semantics more and more?

now, i know i am fundamentally wrong somewhere, and because I've just started id be grateful if someone corrected me where i was going wrong...

thnx