Mathematical induction in one perfect visual. First, you prove something works for a base case (n). Then you prove that if it works for any case (n), it must work for the next case (n+1). Congratulations, you've just proven it works for all cases without checking each one individually. Mathematicians call this elegant. The rest of us call it getting away with the bare minimum of work while still being technically correct.
Induction Is Like

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