Timeline for What's a good notation to show elements of relation composition?
Current License: CC BY-SA 4.0
7 events
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| May 13, 2021 at 1:44 | comment | added | Daniel R. Collins | FWIW when this came in class today and I had to check for transitivity of a simple relation on a set, what came from my hand was something like, $(1,3)$ & $(3,2)$: so $(1,2)$. A bit time-constrained as part of a larger problem, and really felt raw about repeating the element-of statements a bunch of times there. | |
| May 12, 2021 at 19:19 | comment | added | Thierry | @DanielR.Collins You can't get any closer than just overlapping them: $(1,(3),2)$. Maybe with an $S$ and $R$ written underneath for clarity? I don't think it's very good and I prefer Trevor's answer, but this is certainly new and short. | |
| May 12, 2021 at 14:33 | comment | added | Daniel R. Collins | +1 Clearly legitimate and a good thing to consider. However, while it looks viable for one case, when I need to do around a half-dozen for one exercise, then all the repetitive element-of-set parts get a bit frustrating. And I kind of wish the internal bridging elements ($b$) were visually closer together. So I'm leaning towards wanting a (new) shorter notation. | |
| May 12, 2021 at 8:37 | comment | added | Trevor Wilson | I usually handwrite the ampersand as something like $\varepsilon$ with a vertical line through it, which I think looks different enough from $\notin$ to avoid confusion. But the word "and" is always a good choice. | |
| May 12, 2021 at 8:22 | comment | added | Dave L Renfro | Incidentally, and now I'm spending more time here than I wanted to (!), these statements only tell us that certain ordered pairs belong to the composition, and thus something else needs to be used when a student includes an incorrect ordered pair. For class presentations/explanations, however, I guess you handle this by picking elements in $R$ one at a time, and for each such choice, check it's compatibility with each of the elements in $S.$ | |
| May 12, 2021 at 7:47 | comment | added | Dave L Renfro | (+1) I was going to suggest (in a comment, as I don't have time now to discuss issues relating to what to use) "$(1,2) \in R$ and $(2,1) \in S$ gives $(1,1)$", but for teaching purposes "$\ldots (1,1) \in S \circ R$" is probably better, at least in the beginning when students are first learning how to do this. As a personal preference, to reduce the symbol clutter, I would use "and" rather than "&". (Also, I can type "and" quicker than "&", and my hand-writing of "&" is usually not even close to what it's supposed to look like!) | |
| May 12, 2021 at 6:06 | history | answered | Trevor Wilson | CC BY-SA 4.0 |