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comment Examples of open problems solved through short proof
What about Van der Waerden's permanent conjecture? (Maybe it should be called Van der Waerden's temporary conjecture, since it is no longer a conjecture.) I believe the proof of that was easier than expected? Maybe the Dinitz conjecture is another example; I think that was an opoen problem for a few years before a trivial proof was found.
14h
comment can real line be written as a disjoint unions of set with cardinality 5
The axiom of choice is needed to show that the cardinality of $S\times5$ is equal to the cardinality of $S$ for an arbitrary infinite set $S$, but it is not needed to show that the cardinality of $\mathbb R\times5$ is equal to the cardinality of $\mathbb R.$
14h
comment can real line be written as a disjoint unions of set with cardinality 5
If $S$ is a set, can you write $\mathbb Z\times S$ as a disjoint union of $5$-element sets? Can you write $\mathbb Z\times[0,1)$ as a disjoint union of $5$-element sets?
14h
comment can real line be written as a disjoint unions of set with cardinality 5
Can you write $\mathbb Z$ as a disjoint union of sets with cardinality $5$?
1d
comment Cats and Dogs = Idenpedent events
What is the definition if "independent events"? Is it something like "$A$ and $B$ are independent of $P(A\cap B)=P(A)P(B)$"?
2d
answered 1, 5, 9, 13, 17, 21,…
2d
revised Cheap proof that the Sorgenfrey line is normal?
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2d
revised Cheap proof that the Sorgenfrey line is normal?
added 8 characters in body
2d
revised Cheap proof that the Sorgenfrey line is normal?
added 8 characters in body
2d
answered Cheap proof that the Sorgenfrey line is normal?
2d
answered Help understanding incomparable cardinalities
2d
comment Help understanding incomparable cardinalities
What do you mean by "cardinalities that are reached by Cantor's theorem"? How do you compare $2^{\aleph_0},$ the cardinality of the set of all real numbers (or the set of all sets of natural numbers) with $\aleph_1,$ the cardinality of the set of all countable ordinal numbers?
Aug
30
comment null empty set has 2 subsets?
An empty set has only $1$ subset, but $\{\emptyset\}$ is not an empty set. A one-element set $\{a\}$ has $2$ subsets, regardless of what its single element $a$ may be; in this case, $a=\emptyset.$
Aug
30
comment Weird question about natural numbers. Obvious or not?
Why do you say $B=\{7\}$ is maximal? What's wrong with $B=\{1,7\}$?
Aug
29
comment Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
Does "Find groups" mean "Find all groups" or "Find some groups"? Are you looking for a characterization or an example?
Aug
29
revised Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
deleted 14 characters in body
Aug
29
revised Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
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Aug
29
revised Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
deleted 10 characters in body
Aug
29
answered Find groups that contain elements $a$ and $b$ such that $|a|=|b|= 2$ and $|ab|=5$
Aug
28
comment Let $\omega$ be the ordinal of the well ordered set $\mathbb{N}$, what does means $\omega^\omega$?
If the operation in $\omega^\omega$ is ordinal exponentiation, then the elements are not infinite sequences, they are finite sequences; $\omega^\omega=\omega+\omega^2+\omega^3+\cdots.$