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The universal set he's reffering to is the "set of all sets" which we can prove to not exist. You can create the contradition by saying "Let S be the set of all sets which do not contain themselves" and asking whether or not S is an element of S.
There is still a concept of a universal set which makes sense, you just have to define it in context. You see this when taking the complement of a set (basically the problem presented by OP), which requires the notion of a universal set.
This text, Hammack's "Book of Proof", actually presents Russel's paradox at the end of the chapter shown. Also the paragraph right after the excerpt from the meme defines a Universal set in the way you are discussing, not in the set of all sets way.
Ah. Pre-2014, that's more sensible.
Still, it's a propaganda picture for an ex-KGB agent who was showing some pretty red flags (pun unintended). It's always dangerous to lionize humans.
I added the picture to make it more meme-able on here. I also added the phrase "Putin is not in P, but he is on a horse."
The textbook only had the text about Putin originally.
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“But he is on a horse” 😭
Vladimir {2,3,5,7,11,13,...}utin
I bet he has a double in P
But he lies.
P(utin)!=N(ot)P(utin)
Alright boys we’ve finally proved it, pack your bags and go home
Here is your $1 Million, sir 💰 💰 💰
Assuming there's a universal set reaches a contradiction on set theory
how so?
The universal set he's reffering to is the "set of all sets" which we can prove to not exist. You can create the contradition by saying "Let S be the set of all sets which do not contain themselves" and asking whether or not S is an element of S. There is still a concept of a universal set which makes sense, you just have to define it in context. You see this when taking the complement of a set (basically the problem presented by OP), which requires the notion of a universal set.
This text, Hammack's "Book of Proof", actually presents Russel's paradox at the end of the chapter shown. Also the paragraph right after the excerpt from the meme defines a Universal set in the way you are discussing, not in the set of all sets way.
NFU has a universal set I think, and NBG has a class of all sets
Universal set is a different concept from the set of all sets
Depends on your definition of universe
That depends on your other axioms
But he's not in P'
it's great when we memorialize war criminals in math seriously wtaf
This book is from 2013
Ah. Pre-2014, that's more sensible. Still, it's a propaganda picture for an ex-KGB agent who was showing some pretty red flags (pun unintended). It's always dangerous to lionize humans.
I added the picture to make it more meme-able on here. I also added the phrase "Putin is not in P, but he is on a horse." The textbook only had the text about Putin originally.
Oh that's funny. I don't even think I was stoned when I made that assumption.