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Using this proof, you can equate any pair of numbers!

Mathematical Induction

The principle of MI is very useful. It can be used to prove lots of things, including at least one thing that ISN'T EVEN TRUE!

Theorem: A positive integer n is equal to any positive integer which does not exceed it.

Proof by induction:

Case n = 1. The only positive integer which does not exceed 1 is 1 itself and 1 = 1.

Assume true for n = k. Then by assumption k=k-1, as k-1 doesn't exceed k.  Add 1 to both sides and get




This proof is extremely important, because it can be used to equate any pair of numbers.

For example

e = π, by this reasoning:

2 ≤ e ≤ 3, and 2=3, so 3 ≤ e ≤ 3, so e=3.

3 ≤ π ≤ 4, and 3=4, so 3 ≤ π ≤ 3, so π=3.


Edwin McCravy provided this bogus proof.

Related pages in this website

Index of joke proofs

An alternative proof that 2=1

Another alternative proof that 2=1


The webmaster and author of this Math Help site is Graeme McRae.