Some theorems @CihanPostsThms

Posting some theorems, and occasionally other stuff. By @bahran_cihan Joined July 2022

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Some theorems @CihanPostsThms

3 weeks ago

A set X is called amorphous if X is infinite and whenever X = Y ⊔ Z, either Y or Z is finite. Theorem. ZF has models in which there are amorphous sets.

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Some theorems @CihanPostsThms

6 days ago

A short proof of Cantor–Bernstein–Schröder: chiasme.wordpress.com/2013/11/20/a-s…

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Some theorems @CihanPostsThms

2 weeks ago

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Given any year in the commonly used Gregorian calendar, • the last day of February, • April 4 (4/4), • June 6 (6/6), • August 8 (8/8), • October 10 (10/10), • December 12 (12/12) all occur on the same day of the week. For 2025 this so-called Doomsday is Friday.

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Some theorems @CihanPostsThms

3 years ago

In ZF the following are equivalent: (1) ℕ is a Lindelöf space. (2) ℚ is a Lindelöf space. (3) ℝ is a Lindelöf space. (4) The axiom of countable choice holds for subsets of ℝ.

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Some theorems @CihanPostsThms

2 years ago

Let M̅_g,n be the Deligne–Mumford–Knudsen compactification of the moduli space M_g,n of curves of genus g with n marked points. [Canning–Larson–Payne 2023]. Given g ≥ 1, n ≥ 0, TFAE: (1) H¹¹(M̅_g,n; ℚ) ≠ 0. (2) g=1 and n≥11.

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Some theorems @CihanPostsThms

2 years ago

22⋅arctan(24478/873121) + 17⋅arctan(685601/69049993) equals 𝜋/4.

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⚢ nizzy.cc on bluesky 🔆 @technofemme

4 weeks ago

>17 year old trans girl has article written about her mathematical contributions >68 year old creep sexologist (redundant adjective) complains about the article not sexualising her trans women truly are the women of women

Michael Bailey @profjmb

4 weeks ago

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Some theorems @CihanPostsThms

3 years ago

[Papanikolaou 1997]: If the Euler–Mascheroni constant 𝛾 is rational, then its denominator exceeds 10²⁴⁴⁶⁶³.

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Some theorems @CihanPostsThms

4 weeks ago

Let Fₙ be the free group on n generators. Theorem. Given an integer n≥0, TFAE: (1) Out(Out(Fₙ)) = 1. (2) n ≠ 2.

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Some theorems @CihanPostsThms

2 years ago

A topological space X is said to have *countable cellularity* if the size of any collection of disjoint open subsets of X is (at most) countable. Theorem: The statement "If X,Y have countable cellularity, then so does X x Y." is independent of ZFC.

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Some theorems @CihanPostsThms

3 years ago

[Howard 1992]: ZF has a model with the following two properties: (1) Every countable set of nonempty countable sets has a choice function. (2) There is an uncountable set which is the countable union of countable sets.

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Some theorems @CihanPostsThms

3 years ago

More precisely, the following two statements are incompatible over ZF: (1) Every subset of ℝ is Lebesgue measurable. (2) |ℝ| ≥ |ℝ/ℚ|.

Some theorems @CihanPostsThms

3 years ago

More precisely, the following two statements are incompatible over ZF: (1) Every subset of ℝ is Lebesgue measurable. (2) |ℝ| ≥ |ℝ/ℚ|.

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Some theorems @CihanPostsThms

a month ago

Tetris is NP-hard even when restricted to 4 rows. martindemaine.org/papers/ThinTet…

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Some theorems @CihanPostsThms

a month ago

[Cameron–Solomon–Turull 1989]. The height (largest size of a chain) of the subgroup lattice of the symmetric group on n letters is ⌈3n/2⌉ – b(n), where b(n) is the number of 1s in the binary expansion of n.

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Some theorems @CihanPostsThms

2 months ago

Recall that a topological space X is called first-countable at a point x∈X if x has a countable neighborhood basis. [Harley 1973]. There exists a countable Hausdorff space X which is first-countable at no point.

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El Cabbage @AlCabbage045

2 months ago

The chances of AI being able to grift more successfully than Sabine in the near future are much higher than being able to do actual mathematical research

Sabine Hossenfelder @skdh

2 months ago

The chances of AI being able to grift more successfully than Sabine in the near future are much higher than being able to do actual mathematical research