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March 17

Term for one of two things being true

Thanks for the answer about integer math. I have another question about a math term, but it is difficult to explain. Assume you have a collection of things. Only one of them meets the criteria you are looking for. You know that it is exactly one and not two or three. But, there are two that might have the criteria. Whichever one you pick, it is always the other one. I figure this falls under some kind of uncertainty. You know that the attribute or condition you want belongs to exactly one thing, but you can only narrow it down to a small group, preferrably two things. If you try to narrow it down to one, you will always pick the wrong one. I can give a sort of example that I heard once: You are looking for the absolute least interesting person on Earth. You find two people. They have absolutely nothing interesting at all about them. So, you know one of them is the least interesting. If you pick one and call him the least interesting, being the least intesting is something of interest. So, the other guy is actually the least interesting person. But, if you switch who you pick, the least intersting person switches. You can only narrow this down to two people and say one of them is the least interesting. You can't narrow it down to one. I assume there is some well-accepted term for that kind of uncertainty when looking for solutions to mathematical problems. 97.82.165.112 (talk) 14:22, 17 March 2021 (UTC)[reply]

Your example is similar to the interesting number paradox. 247 (number)#In mathematics has an amusing self-reference which was used at Wikipedia:Articles for deletion/247 (number) to support keeping the article. PrimeHunter (talk) 15:09, 17 March 2021 (UTC)[reply]

The law of excluded middle states that every logical proposition is either true or false, so given such a proposition P, one of two things must be true: either P, or its negation ¬P. So consider the proposition P that states, "I am a false proposition". If P is true, then P is a false proposition, and if P is false, it is indeed a false proposition, so it is true. This is known as the Epimenides paradox. A set-theoretical analogue is Russel's paradox. One approach that avoids such paradoxes is to disallow impredicativity, which can be done by requiring that all predicates (definable properties) can be stratified. This also provides a way around the interesting number paradox; the predicate "has an interesting property" or its negation can then not be applied to itself. A general name for an apparent mathematical contradiction is "paradox", where one argument appears to show that some proposition is true, while another argument appears to establish that the same proposition is false. However, in the general case this does not use the conclusion of one branch in the argument of the other branch. --Lambiam 17:15, 17 March 2021 (UTC)[reply]