3 ms·

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 use

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).

oa335 4mo ago
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-epsilon/15460#15460 https://math.stackexchange.com/questions/15455/backwards-eps...
JohnKemeny 4mo ago
It also doesn't make much sense > There exists a raven such that the vector of hours. The vector of hours what?
- brulx126 4mo ago
  The correct statement seems to be: raven = vector of hour hand But maybe that sounded too simple?
frank_nitti 4mo ago
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
dabraham1248 4mo ago
Same. I recalled pipe being used for "such that". But [per wikipedia](https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols#Miscellaneous 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).
- seanhunter 4mo ago
  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.
MarkusQ 4mo ago
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.
- drdeca 4mo ago
  If that’s it, why is it using ∋ rather than ∈? I would expect “Ǝx∈ℕ”.
  - MarkusQ 4mo ago
    Oh, doh! I'd missed that. Yeah, that's...an unusual choice.
- pwdisswordfishq 4mo ago
  > Ǝx∋ℕ "There is an x such that the set of natural numbers is a member of x"?
  - MarkusQ 4mo ago
    Yeah, my bad. My eyes autocorrected it.

oa335 4mo ago

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-epsilon/15460#15460 https://math.stackexchange.com/questions/15455/backwards-eps...

JohnKemeny 4mo ago

It also doesn't make much sense > There exists a raven such that the vector of hours. The vector of hours what?

brulx126 4mo ago
The correct statement seems to be: raven = vector of hour hand But maybe that sounded too simple?

frank_nitti 4mo ago

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

dabraham1248 4mo ago

Same. I recalled pipe being used for "such that". But [per wikipedia](https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols#Miscellaneous 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).

seanhunter 4mo ago
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.

MarkusQ 4mo ago

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.

drdeca 4mo ago
If that’s it, why is it using ∋ rather than ∈? I would expect “Ǝx∈ℕ”.
- MarkusQ 4mo ago
  Oh, doh! I'd missed that. Yeah, that's...an unusual choice.
pwdisswordfishq 4mo ago
> Ǝx∋ℕ "There is an x such that the set of natural numbers is a member of x"?
- MarkusQ 4mo ago
  Yeah, my bad. My eyes autocorrected it.