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Zorn 's lemma is another example.
Probably a better one, from my point. Well, in the sense that IIRC it's equivalent to the separating hyperplane theorem, which I've used over and over.
I met this lemma for the first time when I studied topology in parallel with my studies of physics at Orsay. Mathematics was a little hobby for me at the time. I was amazed to meet him in so many areas of mathematics and so fundamentally
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