Question 424968: prove that 1+1 is equal to 2
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website!
A few simple definitions in Peano terms. 1 is the successor of 0, or S0. 2 is the successor of 1, or so on
Any equation is equal to itself, so we can start with S0 + S0 = S0 + S0 (1 + 1 = 1 + 1)
Any expression of the form A + SB is equivalent to SA + B, so S0 + S0 is equivalent to SS0 + 0. Thusly we can prove that ( )
Since the expressions X + 0 and X are of equal value (by the Peano definition of addition,) SS0 + 0 can be reduced to SS0. Thus, we have proved that 1 + 1 = 2 according to Peano's axioms. (I think... hopefully I haven't skipped over anything or taken an illegal shortcut. It's been a while since I've worked with Peano.)
Algebraically, we can approach the problem somewhat simpler:
Take 
subtract  from both sides, and you see that statement is equivalent to 
Simplifying both sides, you can get  , which is pretty self-evident.
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