Conversation started Jun 11, 2021 at 20:33.
Xander Henderson
Xander Henderson
Jun 11, 2021 20:33
I am writing an exam in which I introduce my students to the notion of a symmetric difference, and ask them to find the symmetric difference of two small sets. However, I don't want to use the term "symmetric difference", as this is very easily Googled. Anyone have any suggestions for a made-up term which means the same thing as the symmetric difference?
Ted Shifrin
Ted Shifrin
From Dr Dolittle: the pushmi-pullyu :)
Xander Henderson
Xander Henderson
Hah!
I loved those books as kids.
Ted Shifrin
Ted Shifrin
It sorta fits!
Xander Henderson
Xander Henderson
It does.
It sounds a little too non-mathy for my taste, but if I can't come up with anything else, it may work.
Ted Shifrin
Ted Shifrin
I like literary allusions
hyper-neutrino
hyper-neutrino
Jun 11, 2021 20:40
remind me; symmetric difference of A and B is {a in A | a not in B} union {b in B | b not in A} ?
Xander Henderson
Xander Henderson
$(A\cup B) \setminus (A \cap B)$.
So... yes.... what you wrote.
Ted Shifrin
Ted Shifrin
$A-B \cup B-A$
Xander Henderson
Xander Henderson
It is all of the stuff in either $A$ or $B$, but not both.
Ted Shifrin
Ted Shifrin
Whence the term.
Xander Henderson
Xander Henderson
@TedShifrin That, too.
hyper-neutrino
hyper-neutrino
Jun 11, 2021 20:42
well basically just something is in the symmetric diff IFF it's in A xor in B ¯\_(ツ)_/¯
my math notation is not so great; i use coding notation sometimes and that's not always accurate
Xander Henderson
Xander Henderson
@hyper-neutrino Yes, that is exactly what it is, if you want to be computer sciency about it.
hyper-neutrino
hyper-neutrino
:P
Ted Shifrin
Ted Shifrin
@hyper That's the interpretation of what Xander wrote.
hyper-neutrino
hyper-neutrino
i mean i could think of more roundabout ways to write it probably :P but hmm, lemme see if i can think of any other wording that'd make sense but not be so googlable
Xander Henderson
Xander Henderson
The "distinguishing set" (as is it is the collection of stuff which makes the two sets $A$ and $B$ different)?
Ted Shifrin
Ted Shifrin
Jun 11, 2021 20:45
That's not bad.
hyper-neutrino
hyper-neutrino
hm, I think that's quite fitting
I might've also suggested something like "the distinct items" or smth, but I think yours makes more sense
copper.hat
copper.hat
Jun 11, 2021 21:25
Elements that are exclusively in one set or the other?
Xander Henderson
Xander Henderson
Jun 11, 2021 21:42
@copper.hat I was looking for something short and pithy and not super duper Google-able.
I settled on the "distinguishing set", and decided on the notation $A \ddagger B$.
Just to be annoying.
Ted Shifrin
Ted Shifrin
May the pushmi-pullyu live on …
Xander Henderson
Xander Henderson
(One of the first assignments that I give to students in calculus is a worksheet where I ask them to read a bunch of definitions, and give them some exercises about understanding definitions; e.g. as planar set is convex if... give an example of a convex set; give an example of set which is not convex; is [this set] convex?, etc).
PM 2Ring
PM 2Ring
It's the complement of the intersection (relative to the union), so you could call it the outersection. ;) FWIW, Python overloads its exclusive-or operator ^ for the symmetric difference.
hyper-neutrino
hyper-neutrino
I mean, a set is just as much a collection of elements as a boolean function from the universal set, so it makes sense to overload boolean/bitwise operators to mean similar things when applied to the membership property :P
it is quite nice - i really like that syntax
very good for code golf too in many cases
Xander Henderson
Xander Henderson
@PM2Ring Heh... I kind of like outersection.
That's cute.
PM 2Ring
PM 2Ring
Jun 11, 2021 21:55
Oh yes. Although in non-golf contexts I tend to prefer using the method syntax rather than the operator syntax, especially for the less common set operations. And the set methods take any (valid) iterable as an arg, whereas if you use the operator syntax, both operands must be sets.
@XanderHenderson Thanks. :) I thought of it a few years ago, but I don't think I've ever mentioned it in public before.
 
Conversation ended Jun 11, 2021 at 21:57.