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Anonymous
ITT: /sci/ proves an open problem 2017-08-20 01:09:23 Post No.
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ITT: /sci/ proves an open problem 2017-08-20 01:09:23 Post No.
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Let [math] \mathscr{F} [/math] be a union closed family, i.e. for all [math] A, B \in \mathscr{F} [/math], the union [math]A \cup B[/math] is also in [math]\mathscr{F}[/math]. Does there always exist some element which is in at least half of the sets of [math] \mathscr{F} [/math]?
Go!
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>>9115681
no, see empty set xd
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Does there exist an odd perfect number?
(A natural number is 'perfect' when it is equal to the sum of its proper divisors.
I.e. 6 = 3+2+1, 28 = 14+7+4+2+1)
[oldest open problem]
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>>9115702
1 = 1. Where’s my Fields Medal?
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Prove that 21 never appears in the Collatz sequence of any odd number other than 21
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(3x+1)/2^y cannot lead to a multiple of 3 since 3x+1 is not a multiple of 3. Obvious when using prime factorisation.
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1=1??? don't get too much excited, it takes 360 pages to prove 1+1=2
http://www.storyofmathematics.com/20th_russell.html
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>>9115906
Multiply 21 by any power of 2.
The result will never be 1 more than a multiple of 3.
Any odd multiple of 3 has that property.
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>>9115702
>Does there exist an odd perfect number?
[math]\varphi\,=\,\frac{1\,+\,\sqrt5}2[/math] is odd (because irrational) yet perfect. Where's my gorillion dollars and eternal pussies?
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>>9116806
Neat. It didn't occur to me to generalize that way.
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