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@sliminality@types.pl

2026-05-08 05:01 UTC

As best you can recall, how did you acquire the knowledge that NOT (x > y) is x ≤ y (i.e. flip sign and strictness)? Please choose the topmost listed answer that applies to you (i.e. even if it has been obvious since birth, if anyone ever taught you directly then please select that option) If someone explicitly taught you, please reply with the setting!

Replies (11)

  • @sliminality@types.pl 2026-05-08 05:06

    FWIW I am in the category of "kept needing it, didn't know, and worked it out" [unsatisfyingly, but I begrudgingly used it going forward because I had no other option]. This was in undergrad, I was not familiar with trichotomy and had not studied real analysis or logic

    Open ##2270284

  • @sliminality@types.pl i answered “obvious” and then i remembered i played through the natural number game 😅

    Open ##2270286

  • @rntz@recurse.social 2026-05-08 05:52

    @sliminality@types.pl other: I still don't know it, because it is false in the contexts I care about (partial orders). counterexample: in sets ordered by inclusion, not {1} {2}. (For real though, I picked "show results" because I honestly don't remember when/how I learned this.)

    Open ##2270287

  • @Taneb@hacksrus.xyz 2026-05-08 05:53

    @sliminality@types.pl I didn't find it obvious, but when I was about 11 or 12 I remember noticing it, unprompted

    Open ##2270289

  • @sliminality@types.pl when the amd manual said jng and jle are aliases

    Open ##2270290

  • @cdrichards@mathstodon.xyz 2026-05-08 10:11

    @sliminality@types.pl learned circa 7th grade (US public school), along with “multiplying both sides of an inequality by a negative number flips the inequality”. Shoutout to Mr. Freiberg, who also taught us the Fizz Buzz game.

    Open ##2270294

  • @soaproot@sfba.social 2026-05-08 20:48

    @sliminality@types.pl When people told me this holds for real numbers in #constructiveMathematics (in fact is often the definition of ≤), I didn't believe them at first. But not only did my collaborators tell me this was a good definition and I read it in the HoTT Book, but I also found it allowed me to prove the expected theorems about ≤

    Open ##2270295

  • @flooey@mastodon.flooey.org 2026-05-08 21:36

    @sliminality@types.pl Huh, I have no idea when I learned that, and it’s surprising to me that so many people do. Is it common people remember where they learned stuff like this? Do people remember when they learned the definitions of words as well?

    Open ##2270296

  • @curtmack@floss.social 2026-05-09 00:10

    @sliminality@types.pl I believe it came up in undergrad formal logic, as an example of how inverting a closed set gives an open set. Not 100% sure if it was there or another class.

    Open ##2270297

  • @jeremysiek@types.pl 2026-05-10 01:46

    @sliminality@types.pl Where’s the option for: too old to remember? :)

    Open ##2415650

  • @krono@toot.berlin 2026-05-10 06:53

    @sliminality@types.pl School. Maths.

    Open ##2415651