Well, a set is an unordered collection of individuals. The unordered collections of individuals that do not contain themselves is an unordered collection of individuals; therefor it is a set....how do we know that "All sets that do not contain themselves as subsets" is a set? — EnPassant
how do we know that "All sets that do not contain themselves as subsets" is a set? — EnPassant
"The set of all sets that do not contain themselves as subsets." — EnPassant
Well, a set is an unordered collection of individuals. The unordered collections of individuals that do not contain themselves is an unordered collection of individuals; therefor it is a set. — Banno
I think Russel's Paradox is superficial and I never believed it "undermines mathematics" which strikes me as an unjustifiably dramatic statement. — EnPassant
In fact it is a trick question because of the way it is stated: "The set of all sets that do not contain themselves as subsets." Why are they calling it a set? — EnPassant
Set A = {a, w}
Set B = {a, x}
Set C = {a, y}
Set X = the set of sets that have {a} as an subset.
Set X = {A, B, C,...}
{a} is in X (because {a} is in A, B, C,...)
therefore X contains X — EnPassant
{a} is a subset of A, B and C, but not a subset of X. — SophistiCat
But the real question I am asking in my first post is: Is the logic I am using coherent? I don't see anything wrong with it, unless you can. — EnPassant
In the following the symbol \x means 'without x' or 'excluding x' — EnPassant
Let Set X = "All sets that do not contain themselves as subsets"\X — EnPassant
And same problemLet Set X2 = (X U X)\X2 — EnPassant
I think this is the correct answer from Snakes Alive: — frank
All sets that do not... — EnPassant
The entity — EnPassant
Misstatement? — frank
The problem is stated as "The set of all sets that do not contain themselves assubsetsmembers." — EnPassant
There is no need to redefine the set. — EnPassant
But that's what you did. — Banno
Is it correct to rewrite this as X = X\X ? Can you translate into English? — tim wood
I get, "the set of all sets that do not contain themselves as subsets" = "the set of all sets that do not contain themselves as subsets" and/but excluding "the set of all sets that do not contain themselves as subsets." And that looks like the empty set. — tim wood
Set X = {{a}, {b}, {c},....{X}} — EnPassant
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.