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Proof techniques #1: Proof by Induction.

This technique is used on equations with "_n" in them. Induction

techniques are very popular, even the military used them.

SAMPLE: Proof of induction without proof of induction.

We know it's true for _n equal to 1. Now assume that it's true

for every natural number less than _n. _N is arbitrary, so we can take _n

as large as we want. If _n is sufficiently large, the case of _n+1 is

trivially equivalent, so the only important _n are _n less than _n. We

can take _n = _n (from above), so it's true for _n+1 because it's just

about _n.

QED. (QED translates from the Latin as "So what?")