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I was thinking about the idea of a set containing itself and that's driving me crazy.

An example of such set is the set of all things that are not turtles, since our set is a "set" then it's not turtle which means it's contained inside itself... but How is this even possible?

let's say set A is included in itself, then outer A just got bigger with another element then inner A gets bigger, then outer A gets bigger and so on. This never ends, it seems like a recursive...

zoro
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  • That being said, there is nothing preventing an object in computer programming from containing a reference to itself, or containing something that contains a reference to itself etc... It is not so much that it anything is getting "bigger" and "bigger" as a result, just that as you drill down you might see something you've already seen before. – JMoravitz Nov 17 '22 at 21:01
  • In javascript for instance, in a browser console type: testobj = {}; testobj.inner = testobj; and explore the object that resulted. Just don't try to expand it fully since you won't be able to. Don't try to run JSON.stringify(testobj) as that will throw errors or try to loop through the children as that can start an infinite loop that will cause your computer to run out of memory. – JMoravitz Nov 17 '22 at 21:06
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    You are not thinking in terms of sets. A set contains another set if it contains all elements from the other set. Clear enough, it does not have to be "bigger". – Vasili Nov 17 '22 at 21:31
  • "the set of all things that are not turtles" . If with "things" you also mean sets , then you run into the same problem as if you ask for the set of all sets , which does not exist. – Peter Nov 18 '22 at 08:04

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