The dating math problem

Upon completion of the algorithm, it is not possible for both Alice and Bob to prefer each other over their current partners.

If Bob prefers Alice to his current partner, he must have proposed to Alice before he proposed to his current partner.

There’s nothing like a math problem to send the internet into a tizzy, is there?

Except that while the internet has a lot of answers, a lot of those answers are wrong.

If Alice accepted his proposal, yet is not married to him at the end, she must have dumped him for someone she likes more, and therefore doesn't like Bob more than her current partner.

If Alice rejected his proposal, she was already with someone she liked more than Bob.

When there are no such pairs of people, the set of marriages is deemed stable.

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