@isAdisplayName

- If you have an End Round card, you can play it only if all four singleton cards are somewhere on the board. If, for example, there is no {X} card on the board, then the End Round cannot be played. There are only three End Round cards in the deck.

When an End Round card is played, all players figure out which expressions have sets that contain their letter. They earn one point for each card in each expression they are in. For example, if Y was only in the first and third rows, with 5 and 8 cards in each, respectively, then the Y player would earn 13 points. Y doesn't earn points for the other two expressions, because Y wasn't an element of the resulting sets.

This game is not particularly well-balanced and is meant to be used as a teaching tool. It is common for all players to discuss together which expressions contain which letters after each turn and often during the turns. The game is interesting both as a 2-player duel and with 3 or 4 players.

2/2

#SetTheory

Playing a set theory card game heavily inspired by #Ergo. #SetTheory

My partner and I were talking about superhero fatigue yesterday, and I realized that part of the problem is that current superpower concepts are oddly limited. There are so many interesting possibilities.

For example, allow me to introduce Lemma, whose powers are based on set theory. Even if your infinite prison has supervillains in every cell, Lemma will find room for infinitely more of them!

#Superhero #Mathematics #SetTheory #Humor #Midjourney

How to prove theorems? ~ Asaf Karagila. https://karagila.org/2023/theorems/ #Math #SetTheory

The unlikely heroes of Cantor’s set theory. ~ Jason Zesheng Chen. https://www.cantorsparadise.com/the-unlikely-heroes-of-cantors-set-theory-44685ef13292 #SetTheory #Math

ChatGPT finally succeeds in writing ZFC in Lean 4, but it wasn't easy. ~ Lars Warren Ericson. https://www.linkedin.com/pulse/chatgpt-finally-succeeds-writing-zfc-lean-4-wasnt-easy-ericson #ChatGPT #ITP #Lean4 #SetTheory #Math

#xkcd #settheory #Astronomy #meme

I have read 1 book( M. R. HOLMES, Elementary #SetTheory with a Universal Set -ISBN 2-87209-488-1)and one thesis ( #Constructivity and #Predicativity: Philosophical Foundations: crosella -2016) thoroughly . Among other things . Now I want to build up on these conceptual foundations, by pursuing this direction, could you suggest me , the relevent literature for this purpose?
#typetheory #categoryttheory

Last Friday I attended the Löb lecture. This is an quadrennial lecture in honour of Martin Löb who founded the logic group here in the University of Leeds after fleeing Nazi Germany as a teenager. See Wikipedia for more information: https://en.wikipedia.org/wiki/Martin_L%C3%B6b

The lecture was given Justin Moore (Cornell). Logic is far from my comfort zone and I don't usually attend logic seminars, but this time I gave it a go because I understood the title: "What makes the continuum ℵ₂?"

This is about how many real numbers there are. Cantor proved that there are more real numbers than natural numbers: |ℝ| > |ℕ|. The Continuum Hypothesis is that there is nothing in between: every uncountable subset of the real numbers has the same cardinality as ℝ.

The cardinality of the natural numbers is denoted ℵ₀ (aleph_0). The next biggest cardinalities are ℵ₁ , ℵ₂ , ℵ₃ , ... So the continuum hypothesis is |ℝ| = ℵ₁. To be precise, this is assuming the standard set theory of mathematics (ZFC, which includes the Axiom of Choice).

The Continuum Hypothesis (CH) is independent of ZFC, so we need arguments outside standard mathematics to decide whether it holds or not. The Justin Moore's argument is that CH has some strange consequences. The only one I understood is that is implies the existence of a bijection ℝ→ℝ that is not monotone on any uncountable set (but I don't have any intuition about this). Assuming CH is false, the next best thing is |ℝ| = ℵ₂ and we can use this to prove some nice theorems ... here is where it got too technical for me. Since we want to prove stuff, Justin Moore argued that we should use |ℝ| = ℵ₂.

#logic #SetTheory #ContinuumHypothesis

Related question: Is Tarski's fixed point theorem constructive, predicative?

Since Tarski's fixed point theorem can be proved by a sort of transfinite induction, how the answer of this question telated to the previous question?
#mathematicallogic #settheory

#settheory folks
you define your choice principle with

Classical set theory: Theory of sets and classes. ~ Taras Banakh. https://arxiv.org/abs/2006.01613 #SetTheory #Math

#CallForPapers #SETS2023 "aims at bringing together researchers interested in set theory, especially to design tools for dealing with set theory, such as interactive or automated theorem provers, proof checkers, theories for general purpose proof tools, constraint solvers, programming languages etc" https://www.lirmm.fr/sets2023/?page=cfp #SetTheory #ITP #ATP

On March 3, 1845, German mathematician Georg Cantor, creator of the set theory was born. Set Theory is considered the fundamental theory of mathematics. He also proved that the real numbers are “more numerous” than the natural numbers, which was quite shocking for his contemporaries that there should be different numbers of infinity.

http://scihi.org/georg-cantor-set-theory-infinity/

#mathematics #settheory #infinity #maths

Good to see a new #video by Aleph 0 after 10 months. This one covers a the continuum hypothesis and a little bit about cohen's forcing. https://www.youtube.com/watch?v=neYulXSt7Tc #settheory

I can tell I've got a good idea for a Pickle story when I can't stop giggling as I think through the details.

I think I've figured out a concrete way to explore sets that are the same vs. sets that are different, the difference between a set and a member of a set, and how you can put together infinitely many sets if you apply some Baby Pickle logic to the task at hand.

#PickleStory #SetTheory #BabyPickleLogic

`Compactness` https://www.youtube.com/watch?v=xiWizwjpt8o

#topology #mathematics #lecture #lesson #topological #setTheory #mathematical #proof #logic #analysis #continuity #infinity #topology

It appears Lyra is an intuitionist mathematician who disagrees with Set Theory.... Or just really doesn't like self referential Sets?
#cats #caturday #CatsOfMastodon #maths #veritasium #SetTheory

#Veritasium - #Math's #FundamentalFlaw

https://www.youtube.com/watch?v=HeQX2HjkcNo&ab_channel=Veritasium

#RussellParadox #BertrandRussell #Philosophy #PhilosophyOfLanguage #PhilosophyOfLogic #Logic #Math #Maths #Mathematics #SetTheory #Sets #Predicates #Subjects #Paradox #LogicalParadox #Contradiction #Contradictions #Incompleteness #IncompletenessTheorem #Goedel #Hilbert

#JeffreyKaplan - #RussellsParadox - A simple #Explanation of a profound #Problem

https://www.youtube.com/watch?v=ymGt7I4Yn3k&ab_channel=JeffreyKaplan

#BertrandRussell #Philosophy #PhilosophyOfLanguage #PhilosophyOfLogic #Logic #Math #Maths #Mathematics #SetTheory #Sets #Predicates #Subjects