Timeline for What's the point of learning equivalence relations?
Current License: CC BY-SA 4.0
28 events
| when toggle format | what | by | license | comment | |
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| Dec 20, 2021 at 2:02 | answer | added | TomKern | timeline score: 0 | |
| Dec 19, 2021 at 23:01 | comment | added | user19239 | Does this answer your question? How to motivate equivalence classes | |
| Sep 11, 2020 at 18:09 | comment | added | Nemo | @StevenGubkin: Good comment in general, but "6^n-1 is a multiple of 5" is perhaps not the best motivating example for anyone who knows how to factor a^n - b^n | |
| Sep 11, 2020 at 4:40 | vote | accept | Daniel R. Collins | ||
| Sep 11, 2020 at 4:36 | answer | added | Daniel R. Collins | timeline score: 3 | |
| Sep 11, 2020 at 0:11 | answer | added | Kevin Carlson | timeline score: 2 | |
| Sep 10, 2020 at 19:46 | answer | added | supercat | timeline score: 2 | |
| Sep 10, 2020 at 19:02 | comment | added | Daniel R. Collins | Unfortunately, in my case, the time constraints on the class are so severe that the lecture section on modular arithmetic is exactly two slides that get maybe 10 minutes total, followed by some exercises. So I'm guessing that my students have a sketchy enough relation to that to not really hit them in the gut in any way. | |
| Sep 10, 2020 at 16:39 | comment | added | Aeryk | You might try emphasizing that saying two things are equivalent is really saying the two things are "the same" in some way. Maybe it's remainder when divided by m (mod m), maybe it's shape but not necessarily size (similarity), maybe it's their spatial component (path-connected), etc. It all boils down to two elements have the same property P. (Notice how easy reflexive, symmetric, and transitive properties are to prove when the statement is "have the same property P"). Summary: An equivalence relation is a sameness. | |
| Sep 10, 2020 at 16:08 | answer | added | Simon | timeline score: -3 | |
| Sep 10, 2020 at 12:09 | answer | added | Pedro | timeline score: 6 | |
| Sep 10, 2020 at 6:17 | comment | added | Michael Bächtold | The rational and real numbers are often defined via equivalence relations. | |
| Sep 10, 2020 at 5:52 | answer | added | Lawnmower Man | timeline score: 11 | |
| Sep 9, 2020 at 16:53 | comment | added | Nick C | You might get some good examples from computer science in the context of a functional programming language, such as Scala. It may not be at the programming level of someone just starting out, but it may give them something to look forward to as their CS career progresses. | |
| Sep 9, 2020 at 16:19 | answer | added | RBarryYoung | timeline score: 3 | |
| Sep 9, 2020 at 16:02 | history | edited | Daniel R. Collins | CC BY-SA 4.0 |
added 4 characters in body
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| Sep 9, 2020 at 15:24 | answer | added | Peter LeFanu Lumsdaine | timeline score: 6 | |
| Sep 9, 2020 at 6:36 | answer | added | Abhimanyu Pallavi Sudhir | timeline score: 2 | |
| Sep 9, 2020 at 4:21 | answer | added | Alexei Levenkov | timeline score: 5 | |
| Sep 9, 2020 at 4:13 | comment | added | Sue VanHattum♦ | I think making the connection between equivalence relations and modular arithmetic is vital. I haven't taught the class often enough yet to have a meatier response, but maybe I can come back to this question in a year or two... | |
| Sep 9, 2020 at 3:03 | answer | added | Misha Lavrov | timeline score: 16 | |
| Sep 9, 2020 at 1:45 | history | became hot network question | |||
| Sep 9, 2020 at 1:18 | answer | added | Alex Gramatikov | timeline score: 1 | |
| Sep 8, 2020 at 23:53 | answer | added | Andrew Sansom | timeline score: 29 | |
| Sep 8, 2020 at 23:28 | answer | added | guest | timeline score: -4 | |
| Sep 8, 2020 at 19:45 | comment | added | Daniel R. Collins | @StevenGubkin: We do, briefly. But I fear that response would be too abstract to satisfy my students on this question. (E.g., I also get "why do we learn modular arithmetic?", and at least with that I can point to concrete applications like hash values, pseudorandom numbers, check digits). And no induction problem is trivial for my students, to most they're all equally opaque (e.g., most leave it blank on final). | |
| Sep 8, 2020 at 18:10 | comment | added | Steven Gubkin | Do you learn modular arithmetic in these courses? Knowing that congruence is an equivalence relation, and that the operations of addition and multiplication respect this equivalence relation, is essential and readily understandable. Arguing that 6^n-1 is a multiple of 5 is a challenging induction problem without these facts, but it a trivial induction problem with these facts, for instance. | |
| Sep 8, 2020 at 17:45 | history | asked | Daniel R. Collins | CC BY-SA 4.0 |