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Martin Sleziak
Martin Sleziak
9:48 AM
Some discussion about set theory in the main chat room:
in Mathematics, 26 mins ago, by DHMO
what is the theorem called? $|k| \ge |\Bbb N| \implies |k \times k| = |k|$
in Mathematics, 25 mins ago, by DHMO
Can I prove that $|k \times k| = |k| \implies |2^k \times 2^k| = |2^k|$?
in Mathematics, 18 mins ago, by DHMO
so I can prove that $|\Bbb R \times \Bbb R| = |\Bbb R|$ without invoking AoC!
Although I guess they were answered there relatively satisfactorily.
 
Martin Sleziak
Martin Sleziak
10:20 AM
This question seems interesting: If we only work with beth number, which of the laws for cardinal arithmetic are provable in ZF and which of them need (some form of) choice?
in Mathematics, 13 mins ago, by DHMO
among the results listed here which still needs AoC when restricted to the beth numbers?
It seems that $a+a=a\cdot a=a$ should be relatively easy to show if $a=2^b$.
I am not sure what to say about comparability.
 
 
5 hours later…
Martin Sleziak
Martin Sleziak
2:56 PM
 

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