Lemma, proposition, theorem or corollary are different types of mathematical claims with different levels of importance and difficulty. Logically, these claims are same as all of them need a valid proof to be deemed true.

1. Lemma: easily proved and least interesting claim that can be used to prove other claims …

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Natural numbers are numbers that follows Peano axioms.

Peano Axiom

1. 1 is a natural number.
2. If \(n\) is a natural number then \(n++\) is also a natural number.
3. 1 is not a successor of any natural number. Hence, \(n++\neq 1\) for every natural number \(n\).
4. For two natural numbers …

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