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=k1, as k1 doesn't
exceed k. Add 1 to both sides and get
k+1=k.
QED.



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.
References
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.