In my mind they’re literally the same/similar and I cannot wrap my head around it
Tried googling but didn’t help
Please can someone explain the difference?
In: Mathematics
Proof by induction proves that one case is true then proves that if it is true for X, it is true for another case (often X+1).
By proving those two things, you can prove it’s true in an infinite number of cases.
Proof by exhaustion proves something is true for every possible case by considering every case or type of case. This is often simpler than proof by induction, but can be more limited.
If you’re proving something is true for all numbers 1-100, proof by exhaustion and a computer is great. If you want to prove it for all natural numbers, you want proof by induction, or some way to narrow it down to use proof by exhaustion (such as modulo mathematics, eg: considering the cases where is even and where it is odd).
Sometimes you might even combine them and use a proof by exhaustion that uses induction for some of the types of cases.
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