Proof by example can be a proof. It depends on the theorem statement.

Sure — but, given the proof by contradiction, the examples would then illustrate the trade offs that the theorem forces.

Proove that you can walk. Walk. Prooved by an example. Basically to prove that something exists or that a property is not valid for every element of a set, you can proove with an example.

Proove that you can't walk. Don't walk.

Hmmmmmm.

Of course you can prove something exists by an example. And you can prove a property does not always hold with a counter example.

But if you want to prove that something doesn't exist, or a property always holds, then you shouldn't be looking for examples.

This is exactly what I've said. My initial "proof by example" was an answer for the op's statement:

> Proof by example or analogy is not a proof.

So as you also said "Of course you can prove something exists by an example".

To answer this: > Proove that you can't walk. Don't walk.

As I said, proof by example works only

> to prove that something exists or that a property is not valid for every element of a set.

Divide your lifetime in seconds. With that, you're trying to proove with the property "walk" isn't valid for every element of the set lifetime. To proove that the property can't walk dosen't hold for every element of the set, just show an example of second while you were walking and you're done.

The reverse proves something different. If you walk, you've proved that you CAN walk. Not walking is not a proof for lack of ability. It does however give a possible counter example to the assumption "If you can walk, you will walk"

This sounds wrong to me. Do visual proofs not count?