I don’t think I have ever seen ∋ used to mean “such that” so I was very confused until I got to the explanation (as it were; why CONTAINS AS MEMBER is being used to mean “such that” is never explained).
I don’t think I have ever seen ∋ used to mean “such that” so I was very confused until I got to the explanation (as it were; why CONTAINS AS MEMBER is being used to mean “such that” is never explained).
as a math major i had the same confusion; for such that i use "s.t.". but apparently peano used ∋ to mean such that:
https://math.stackexchange.com/questions/15455/backwards-eps...
Interesting, my experience in classes using set theory was the opposite, where ∋ only meant “such that” and ∈ only meant “is a member of”.
Learning programming syntax at the same time made it frustrating to learn that math symbols were less strictly defined and less universal, that it was best to write proofs/derivations/etc in plain English in many cases instead of the neat symbols
Same. I recalled pipe being used for "such that". But [per wikipedia](https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo...), that's specifically "set-builder notation", and the _last one_ of the twelve instances of the string "such that" on the page (though I don't know if they're ordered by usage, "alphabetically", or what).
Yeah in my experience (and on my bookshelf), I see “:”, “|”, “s.t.” And the words “such that” or “with” (this often works in context for lots of properties) and I have literally never seen that inverse membership sign before.
Not a huge fan of quantifier symbols in published notation. For example I use backwards E all over the place in my notes, but in everything I typeset I say “there exists”. Mathematics is supposed to be written in complete sentences anyway so you are going to have some words, so this doesn’t seem a particularly useful two words to turn into a symbol.
It also doesn't make much sense
> There exists a raven such that the vector of hours.
The vector of hours what?
The correct statement seems to be: raven = vector of hour hand
But maybe that sounded too simple?
This isn't quite what's going on. A better reading might be "which is a";
"Ǝx s.t. x∈ℕ" (there exists an x such that x is in the naturals) is just being shortened to "Ǝx∋ℕ" (there exists an x in the naturals), or there exists an x which is in the naturals.
It's not really that different from the normal usage.
If that’s it, why is it using ∋ rather than ∈? I would expect “Ǝx∈ℕ”.
Oh, doh! I'd missed that.
Yeah, that's...an unusual choice.
> Ǝx∋ℕ
"There is an x such that the set of natural numbers is a member of x"?
Yeah, my bad. My eyes autocorrected it.