Tagged Questions
4
votes
2answers
133 views
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 ...
-2
votes
2answers
189 views
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 ...
3
votes
3answers
105 views
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 ...
2
votes
2answers
128 views
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 ...
18
votes
3answers
977 views
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 ...
2
votes
2answers
238 views
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 $f$, ...
4
votes
1answer
154 views
How is the Cantor's paradox resolved in the ZFC system?
How is the Cantor's paradox resolved in the ZFC system?
Thanks.
