Let A be any set. We define B such as:

Can it be that ? No.

Proof by contradiction.

Assume .

- If then by the definition of B:

. Contradiction. - If then by the definition of B:

. Contradiction.

Therefore .

Credits for the succinct proof.

Random stuff that I care about

Let A be any set. We define B such as:

Can it be that ? No.

Proof by contradiction.

Assume .

- If then by the definition of B:

. Contradiction. - If then by the definition of B:

. Contradiction.

Therefore .

Credits for the succinct proof.

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