# Principles of proof writing

Principle 2.1 (First Principle of Mathematical Induction). Let S(n) be a statement about
integers for n  $\in$ N  and suppose S(n0) is true for some integer n0. If for all integers k with
k n0, S(k) implies that S(k + 1) is true, then S(n) is true for all integers n greater than
or equal to n0.

Equivalence relation:

1. Reflexive.
2. Symmetric.
3. Transitive.
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