Can you prove that 1+1=2?
If you define the natural numbers with the Peano-axioms, you can define the addition of two numbers (recursively) as:
So in this case we have 1 + 1. With 1 being the successor of 0, so 1=0' we can write that as:
1 + 1 = 1' = 2
1. n + 0 = n
2. n + m' = (n + m)'
Where n' is the successor of n.So in this case we have 1 + 1. With 1 being the successor of 0, so 1=0' we can write that as:
1 + 0'
With the second equation, we get:1 + 0' = (1 + 0)'
With the first equation now, we get that 1 + 0 = 1
, so:(1 + 0)' = (1)' = 1'
And we know the successor of 1, which is 2. Thus:1 + 1 = 1' = 2
