What is Zero? (Set Theory Definition)

An explanation of how zero is defined in set theory for the purpose of constructing the Peano Postulates.
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Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy, The Oxford Companion to Philosophy, The Routledge Encyclopedia of Philosophy, The Collier-MacMillan Encyclopedia of Philosophy, the Dictionary of Continental Philosophy, and more! (#settheory #peano)

[@tracylynn1461]

The hero? 😂

[@siddharthabanerjee6155]

Hey, I just discovered your channel from the Map of Philsophy video, and it was awesome. Could you please tell what font you use for the text in your videos? I really like it and haven't been able to find it.

[@tomholroyd7519]

Zero is the boundary between true and false. #RM3 can be constructed so that boolean (2 valued) logic uses +x for true and -x for false, and 0 means both true and false. RM3 is the best logic you can use, because it solves almost all paradoxical sentences, such as the Liar.

[@InventiveHarvest]

Zero is not equal to the null set. The null set is a set that does not have any members, including zero, which is a number.
We could say that zero is the cardinality for the null set, but to do that, we would have to be able to count (which we can't do because we don't have the natural numbers yet).
All we can do is use the power of naming to call zero the amount of nothingness.

[@gabitheancient7664]

in the modern construction of the naturals, since zf, the natural number 0 is defined to be the empty set
the actual idea is to associate each number to the ones that come before it, like 3 = {0,1,2} and 4 = {0,1,2,3}, so naturally, to have a base, 1 = {0} and 0 = {}
also yeah 0 is not a member of the empty set obviously it IS the empty set

[@InventiveHarvest]

@@gabitheancient7664 if 0 =[], then 0 is a set, not a number.

[@Dayglodaydreams]

Das Nihl.