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Post AUIbB2ODP2k38CPVS4 by [email protected] |
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More posts by [email protected] |
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Post #AUHSNY8o5GpyKu8Pp2 by [email protected] |
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Leibniz based his approach to calculus on infinitesimals - numbers that are big… |
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Post #AUHUSry3zoOnBSm3Fo by [email protected] |
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@johncarlosbaez This has actually been tried (very few times) in actual classro… |
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Post #AUHVXTETULuDs3CxaC by [email protected] |
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@johncarlosbaez non standard analysis is very cool, but I sometimes wonder if t… |
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Post #AUHWtv3AqM0QTGBruK by [email protected] |
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@johncarlosbaez at least one of my college professors taught us some calculus u… |
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Post #AUHWtv7mZDgyhYLY5g by [email protected] |
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@tsrono - it's very unusual, at least in math departments. Physicists ofte… |
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Post #AUHX68UIi0V7cbhimu by [email protected] |
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@RobJLow - for some reason the second book I read on any subject is always easi… |
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Post #AUHY0Xe8MBDrrmCS7U by [email protected] |
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@johncarlosbaez when I learned about hyperreal numbers there was something that… |
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Post #AUHY0Xj63jC07AWPr6 by [email protected] |
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@loke - the main "catch" is that to do serious math with the hyperrea… |
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Post #AUHa0OoxMxbiP3K1bM by [email protected] |
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@johncarlosbaez oh, interesting! i found the epsilon concept really intuitive, … |
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Post #AUHa0OtD790gcFJQES by [email protected] |
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@tsrono - note you're not using infinitesimals if you treat ฮต as an ordina… |
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Post #AUHaX7gy4hoUpqBnLU by [email protected] |
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@johncarlosbaez Knuth has a light hearted โdialog between two peopleโ book … |
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Post #AUHailC5Y272X9IKS8 by [email protected] |
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@johncarlosbaez For those who are new to this: already in 1934, Thoralf Skolem … |
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Post #AUHailGhGtnalRS0dU by [email protected] |
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@SylviaFysica - thanks! I bet I'll enjoy reading about their history in th… |
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Post #AUHayR3sAT5Oj8vUau by [email protected] |
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@johncarlosbaez is this th noneuclidean geometry stuff? I remember reading a bo… |
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Post #AUHayR8TtKlwxR5AmG by [email protected] |
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@barrygoldman1 - no, this has essentially nothing to do with noneuclidean geome… |
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Post #AUHdJ2stS7kBjUkKH2 by [email protected] |
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@johncarlosbaez If I understand correctly, hyperreals are much more complicated… |
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Post #AUHeyX6Y6CwTHoTpK4 by [email protected] |
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@ohThef7y - yes, I was telling @loke here that redoing all of math based on hyp… |
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Post #AUHzkFSgzoztYErq88 by [email protected] |
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@jayalane @johncarlosbaez Those are slightly different numbers; those are the _… |
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Post #AUHzkFXIiggRmX1WJU by [email protected] |
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@sstadnicki @jayalane - yes, there are a lot of different systems that include … |
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Post #AUICcwymc6zRbdjBbs by [email protected] |
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@johncarlosbaez Bourbaki ruined everything. |
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Post #AUICcx3OKyfzpvsrnE by [email protected] |
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@wrog - actually I think Bourbaki's books are great for what they are. But… |
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Post #AUICtR32aReNUna18S by [email protected] |
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@vsaraph Not really; one issue is that to the extent that Cantor's infiniti… |
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Post #AUICtR7IKd3LhzZPlY by [email protected] |
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@sstadnicki @vsaraph - Steven answered the question as well or better than I wo… |
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Post #AUIaJ5c3CfGhUS9p7A by [email protected] |
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@johncarlosbaez thanks. As someone who doesn't do much, if any, rigorous ma… |
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Post #AUIaJ5gevWxFikJVIW by [email protected] |
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@loke wrote: "I take your statement that it's OK to use hyperreals as … |
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Post #AUIaN59wpY97F6usk4 by [email protected] |
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@loke @johncarlosbaez This sounds like the opposite! If you're not trying t… |
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Post #AUIaN5EYYPpfTP4YvQ by [email protected] |
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@Robotbeat @loke wrote: "This sounds like the opposite! If you're not … |
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Post #AUIavLzSlBOfHxM0vI by [email protected] |
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@johncarlosbaez Well that's pretty interesting, and yeah, that DOES seem a … |
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Post #AUIavM44U35DWFVh6e by [email protected] |
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@Robotbeat - none of math is about "weird rules you need to memorize"… |
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Post #AUIbAu5UGn0XNnaR9M by [email protected] |
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@johncarlosbaez I feel obligated to plug Goldblatt's ๐ฟ๐๐๐ก๐ข๏ฟฝ… |
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Post #AUIbB2ODP2k38CPVS4 by [email protected] |
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@hallasurvivor @johncarlosbaez Rob Goldblatt was the supervisor for my Master&#… |
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Post #AUIbB2Sp7uQbMUZBdQ by [email protected] |
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@RanaldClouston @johncarlosbaez Absolutely! I tend to advise students away from… |
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Post #AUIbB2X4s5pZZgYaGW by [email protected] |
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@hallasurvivor @RanaldClouston - all the expert category theorists I know compl… |
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Post #AUJHsXBcyLl9AnwiMy by [email protected] |
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@johncarlosbaez @loke This would lead to an immediate question of whether it de… |
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Post #AUJPomEhsL4uK96blg by [email protected] |
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@johncarlosbaez All true. Still find the algebraic derivation of derivative rul… |
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Post #AUJPomIxcWTsXL60Om by [email protected] |
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@Robotbeat - agreed! |
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Post #AUJRi83cXvTxslsUeO by [email protected] |
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@ohThef7y @loke - as you say, there are nonisomorphic versions of the hyperreal… |
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Post #AUPIMP3wuI0Pc6MAqG by [email protected] |
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@johncarlosbaez I don't want to sound lazy but where could I find spelled … |
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Post #AUQhsddiwB426OW9Eu by [email protected] |
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@leemph - you can see the hyperreals and the "dual numbers" (the real… |
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Post #AUQow4cNmvoaK1TWzI by [email protected] |
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@johncarlosbaez Thank you for the links! I'll read them carefully.I know th… |
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Post #AURecFI1b4ERFCosXQ by [email protected] |
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@leemph - I don't know a universal property of the hyperreals, which would … |
