# Tagged Questions

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### The set of all infinite binary sequences

Suppose that we have the set $S$ of all possible infinite binary sequences $s_i$ (a sequence is simply an ordered set): $$S=\{s_1,s_2,s_3,\ldots \}$$ where the sequences $s_i$ are like ...
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### Does a complement contain itself?

I think it is safe to assume many sets do not contain their complements. {1, 2} for example. Now, by the definition of complement, that would mean the complement would have to contain itself. This ...
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### Why is the hypergame not simply well founded?

According to Cameron, the hypergame paradox proceeds as follows: A game is considered as well founded if ANY play of the game ends in a finite number of moves. A hypergame is where the first player ...
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### Can one come to prove Cantor's theorem (existence of higher degree of infinities) FROM Russell's paradox?

I have been thinking about this: One can arrive at Russell's paradox from Cantor's argument, but can we go the other way round, i.e., can we prove Cantor's diagonal argument(often referred to as ...
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### difference between class, set , family and collection

In school I have always seen sets. But I was watching a video the other day about functors and they started talking about any set being a collection but not vice-versa and I also heard people talking ...
### An unwanted property of the set $T=\{x,\{x\} \}$
Let $T$ be $T=\{x,\{x\},y \}$ and let $f:A\rightarrow T, \ f(a):=x$, where $A=\{a\}$. Define $B=\{x,y \}$. Now a weird thing happens: We should have that $x \in f(f^{-1}(B))$ by construciton of $f$, ...