# Sets vs. Plain-language Groups **URL:** \ **Category:** Factual Questions\ **Created:** [June 5, 2026, 2:50pm UTC](https://boards.straightdope.com/t/sets-vs-plain-language-groups/1030636 "2026-06-05T14:50:04Z")\ **Posts on this page:** 5\ **Page:** 2
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 6, 2026, 1:41pm UTC](https://boards.straightdope.com/t/sets-vs-plain-language-groups/1030636/21 "2026-06-06T13:41:30Z")
OK, I just looked it up, and the Tits Alternative is one of those eponyms that @Hari_Seldon mentioned, named after a mathematician named Tits. It’s about group theory, and does not, so far as I can tell, have anything to do with mammaries. The Hairy Ball Theorem and the Ham Sandwich Theorem do talk about actual hairy balls and (suitably-abstracted) Ham Sandwiches, though, and the Monster Group is very big. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [June 6, 2026, 9:09pm UTC](https://boards.straightdope.com/t/sets-vs-plain-language-groups/1030636/22 "2026-06-06T21:09:35Z")
Just for the record, the ham sandwich theorem, when applied to an actual ham sandwich says it is always possible to cut it by a straight slice in such a way that each piece has exactly half the ham and half the bread. The hairy ball theorem says that if a ball has a hair of non-zero length at each point, It is not possible to comb it so that each hair lies flat (tangent to the ball). In technical terms there is no nowhere vanishing tangent vector field on a sphere. Or there is always at least one place on earth with no horizontal wind. ---
**Author:** ![Q.Q.Switcheroo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/q.q.switcheroo/32/5713_2.png) [@Q.Q.Switcheroo](https://boards.straightdope.com/u/Q.Q.Switcheroo)\ **Post date:** [June 7, 2026, 12:31am UTC](https://boards.straightdope.com/t/sets-vs-plain-language-groups/1030636/23 "2026-06-07T00:31:32Z")
> [@Hari\_Seldon](#): > > Just for the record, the ham sandwich theorem, when applied to an actual ham sandwich says it is always possible to cut it by a straight slice in such a way that each piece has exactly half the ham and half the bread. Is that before or after it’s indicted by a grand jury? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 7, 2026, 6:18pm UTC](https://boards.straightdope.com/t/sets-vs-plain-language-groups/1030636/24 "2026-06-07T18:18:24Z")
> [@Hari\_Seldon](#): > > Just for the record, the ham sandwich theorem, when applied to an actual ham sandwich says it is always possible to cut it by a straight slice in such a way that each piece has exactly half the ham and half the bread. Half of the ham and half of each slice of bread. And it’s an abstracted ham sandwich because the ham and each slice of bread can each be any three-dimensional shape at all (or at least, any three-dimensional shape with defined volume, significant if you’re silly enough to use the Axiom of Choice and therefore allow for the possibility of shapes without defined volume). ---
**Author:** ![Gordon\_G](https://avatars.discourse-cdn.com/v4/letter/g/3da27b/32.png) [@Gordon\_G](https://boards.straightdope.com/u/Gordon_G)\ **Post date:** [June 15, 2026, 9:28am UTC](https://boards.straightdope.com/t/sets-vs-plain-language-groups/1030636/25 "2026-06-15T09:28:58Z")
> [@xtenkfarpl](#): > > It seems to me that the concept of a ‘set’ is pretty abstract. It developed in the late 19th and early 20th century as a way to try to formalise mathematics as a branch of logic. > > Seemed quite intuitive for a while, until Russel’s paradox appeared. There’s a famous case where Gottlob Frege was about to publish a definitive book on set theory, when Russel’s letter appeared. Russell’s paradoxical set (whose members are all sets not contained in themselves) might be a useful set! Have your cake and eat it to by adopting _Inconsistent Mathematics_. > **[Inconsistent Mathematics (Stanford Encyclopedia of Philosophy)](https://plato.stanford.edu/entries/mathematics-inconsistent/)** [Previous page](https://boards.straightdope.com/t/sets-vs-plain-language-groups/1030636.md?page=1)