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 Dec 12 comment Notation to define family of sets from mapping to set of pairs @AsafKaragila No idea what you're making a fuss about. I have a mapping from a key to a pair. The order is there, both in the fact that it is a tuple, and also in the semantics of what I am using this in. I said you can see it as you want because if the second version made it easier, I might be able to change one to the other. You are now introducing stuff I didn't even mention. Dec 11 accepted Notation to define family of sets from mapping to set of pairs Dec 11 comment Notation to define family of sets from mapping to set of pairs Thanks for your explanations. I guess I actually can convert my tuples to sets in reality first, and use the concept of a choice function as you indicated. Dec 11 comment Notation to define family of sets from mapping to set of pairs You can see it as you want. Yes it is an ordered tuple in actual fact, not that relevant to this problem I have though. I can probably reformulate it as $K \to \mathbb{R} \times \mathbb{R}$ if it makes a difference. Dec 10 asked Notation to define family of sets from mapping to set of pairs May 21 comment Set builder notation for matching element pairs Thanks for your answer. Do you think the multiset union symbol $\uplus$ is clear and popular enough to use on its own? Or would I need to write a sentence or even define it (that it adds the sum together). May 21 accepted Set builder notation for matching element pairs May 20 comment Set builder notation for matching element pairs @copper.hat Thanks. Is there any other (less cumbersome) notation I could use? May 20 comment Set builder notation for matching element pairs @copper.hat I get it now... but if $S$ is not a set, the set builder notation is not applicable I guess. What would you use instead, if $S$ was a multi-set? May 20 comment Set builder notation for matching element pairs @copper.hat In my particular case I am collecting the 'b' part. (In reality they are numbers that I will need to sum over with $\sum$ but as such it is unrelated to this problem.) To use the surname and name example, the pairs are ('murphy', 'joe') and ('murphy', 'tony') and I want ('joe', 'tony'). In the case $S$ is not a set but a bag, if there happens to be ('murphy', 'joe'),('murphy', 'joe'),('murphy', 'tony') I want ('joe','joe','tony'). May 20 comment Set builder notation for matching element pairs @hardmath Well in my particular case order does not matter (although it would be useful to learn how to do it with a sequence too I guess :) ). So yes the correct definition is a bag or multi-set. May 20 comment Set builder notation for matching element pairs @copper.hat I don't want to count the number of times. I want a list of the actual elements. Imagine it is a pair of 'surname' and 'name' and we're extracting the list of 'names' with the same 'surname'. May 20 comment Set builder notation for matching element pairs @hardmath Yes. Thats why I said $S$ becomes a list and not a set, you can see it as a sequence. But I don't know if there is any elegant mathematical notation to iterate through and extract the list (or bag or whatever) of $b$ items. May 20 asked Set builder notation for matching element pairs May 11 accepted Right notation to recurse over a sequence or list May 11 comment Right notation to recurse over a sequence or list Thanks. Yes I was looking for something like that, but I wasn't sure if the colon was accepted mathematical notation for the head / tail of a list. (In Haskell its written :, in Scala its written ::). To me it seems a bit more correct, because $xs$ can be the empty list. May 10 comment Right notation to recurse over a sequence or list Regarding the right fold (vs left fold), the result would be different though right? I want to first apply $f()$ to $x_1$, then $x_2$ etc. while with the left fold it applies $f()$ to $x_n$ first. May 10 comment Right notation to recurse over a sequence or list Thanks. My concern is that if $n = 1$ then $x_1, ..., x_{n-1}$ becomes invalid, because $n-1$ becomes $0$, so $x_1, ..., x_0$ is incorrect, when it should be the empty sequence. I once saw somewhere a different syntax, but I cannot recall where, but it was something like $F(p, h:t) = F(t, f(h, a))$ but I am not sure if it was with the colon and whether it is correct. May 8 awarded Critic May 7 revised Right notation to recurse over a sequence or list added 3 characters in body