Turtlewing wrote:1+1=2 is part of the defenition of addition (when applied to most common number systems). Asking to prove 1+1=2 without using the deffenition of 2 is asking for something like:
let there be a thing
let there be another thing
by the defenition of addition there are now more than 1 things, and less than 3 things. let's call this case "there are 2 things".
(prety stupid and useless, but to drive home the stupid and useless I made it seems even less formal and well thought out in the original post)
Asking for a proof of 1+1=2 without using the defenition of _addition_ on the other hand is actually "prove addition for the natural numbers". which is still pretty pointless since the proof of addition is basicly just a restatment of the defenition of counting, and counting is generally held to be a fundamental postulate that is well verified by observation. So the proof will likley involve a practical demonstration of counting, but at least this question is driving that something that is worthwile to do every now and then (questioning your assumptions).
Oh my god, why can't you spell? Get Firefox, ffs, it has a built-in spellchecker.
Also, there is a formal mathematical proof that 1+1=2. If you seriously think it's as inane as you've made it out to be, try Google. It's your friend.