Proof of Identity Element
Definition states directly that 0 is a right identity. We prove that 0 is a left identity by induction on the natural number a.
For the base case a = 0, 0 + 0 = 0 by definition . Now we assume the induction hypothesis, that 0 + a = a. Then
- 0 + S(a)
- = S(0 + a)
- = S(a)
This completes the induction on a.
Read more about this topic: Proofs Involving The Addition Of Natural Numbers
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