Question :
Proof that 1 + 1 = 2
Answer :
We know that,
1. a + 0 = a
2. a + s(b) = s(a + b)
3. if a = b, b = c, so a = c
And assume that,
1. s(0) = 1
2. s(s(0)) = 2
3. s(s(s(0))) = 3
So,
1 + 1
Change 1 into s(0),
1 + 1
= s(0) + s(0)
Insert the first s(0) into second s(0),
s(0) + s(0)
= s(s(0) + 0)
Cancel out the 0,
s(s(0) + 0)
= s(s(0))
Change s(s(0)) to 2,
s(s(0))
= 2
Hence, it proofed that 1 + 1 = 2
