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Post AwrpPLIDMnavAPvyoi by [email protected] |
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More posts by [email protected] |
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Post #Awr4r4sLIt84VpYXHU by [email protected] |
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When people claim 0.9999.... is not equal to 1, you can explain why they're… |
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Post #Awr71EqVHy4IEsfWF6 by [email protected] |
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@johncarlosbaez @OscarCunningham I love hyperreal numbers! They saved my thesis… |
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Post #Awr9s2hfMgQZpsqFNI by [email protected] |
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@attilakinali - wow, I'm impressed that you actually used them to prove a t… |
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Post #AwrDLn9U34Sq9cjKmu by [email protected] |
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@johncarlosbaez @OscarCunningham When people claim that 0.999... is not equal t… |
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Post #AwrLCsDCfK9msHjDl2 by [email protected] |
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@maxpool - how could anyone dare disagree, after that framing? 🙃 Oh wait,… |
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Post #AwrQTzybY9gleKswqm by [email protected] |
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I've always wondered what happens if you allow metrics taking values in hyp… |
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Post #AwrW7V36SLcz5Ge0m0 by [email protected] |
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@Bushy - you can develop the theory of manifolds and metrics and so on using th… |
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Post #AwrWPKxghQSh0kcIsq by [email protected] |
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@maxpool one way to dispense with this unspoken assumption is by observing that… |
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Post #AwrWPL44JhZ9KXbOpU by [email protected] |
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@ccppurcell @maxpool - yes, if I had to teach kids math I'd like to get the… |
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Post #AwrcXnXOwCbdgCjtNw by [email protected] |
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@johncarlosbaez @maxpool I was never the average grade school math student, but… |
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Post #Awrcwv85qg6ASssgF6 by [email protected] |
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@johncarlosbaez Wonderful timing on this post! I've been discussing infinit… |
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Post #AwrcwvE7UGv2lZhUdU by [email protected] |
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@pmbrent - I'm sure you can use it to exacerbate their confusion. 😏 I… |
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Post #Awrh0qHiCfKSPiVPCC by [email protected] |
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@johncarlosbaez @OscarCunningham > The hyperreals contain different sizes of… |
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Post #Awrho6XaYIf71LQCwa by [email protected] |
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@johncarlosbaez @ccppurcell This is interesting, apparently there is a step in … |
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Post #AwriEVdXrt6UNrna08 by [email protected] |
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@johncarlosbaez @OscarCunninghamI want to say the surreals are conceptually sim… |
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Post #Awrj0XtSmTJPHc9LGK by [email protected] |
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@johncarlosbaez @OscarCunningham A reminder that the reason we don’t have u… |
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Post #AwrklhwfKJIi1RhSt6 by [email protected] |
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@ccppurcell @maxpool I've tried this, it doesn't work, and there are go… |
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Post #Awrkli5WnMOESvqXhY by [email protected] |
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@zwol @ccppurcell @maxpool Start with a cake, and in the first day eat 9/10 of … |
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Post #AwrkliBuPdUgmipdeC by [email protected] |
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@MartinEscardo @ccppurcell @maxpool Will be rejected, for exactly the same reas… |
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Post #AwrkliIzzHAJ8i9IhM by [email protected] |
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@zwol @ccppurcell @maxpool Have you tried to ask them to compute the subtractio… |
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Post #AwrkliP1crzBROy75k by [email protected] |
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@MartinEscardo @ccppurcell @maxpool Yes, they say the difference is 0.000...001… |
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Post #AwrkliV3GSo3k5mvU8 by [email protected] |
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@zwol writes " Yes, they say the difference is 0.000...001, where the stri… |
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Post #Awrklib4u3cw2mbjsW by [email protected] |
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@MartinEscardo @zwol - In the hyperreals we do have various numbers like 0.00… |
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Post #Awromdwe5JthioONdI by [email protected] |
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@johncarlosbaez @ccppurcell @maxpool I like the distinction of smart vs interes… |
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Post #AwrpMckjzgzoRwysJk by [email protected] |
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@BRicker @ccppurcell @maxpool - for me too, the New Math was very beneficial. … |
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Post #AwrpPLIDMnavAPvyoi by [email protected] |
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@johncarlosbaez I think the essence of the problem is that students (and someti… |
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Post #Awrpi0vDKVG9UQ4xjk by [email protected] |
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@MartinEscardo - True. And I think that's okay here, because I don't … |
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Post #AwrsMI5J8c5AD88L0C by [email protected] |
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@johncarlosbaez Yes, I agree with explaining things intuitively first. Intuitio… |
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Post #AwrzIu4MfWoQXV1Z8y by [email protected] |
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@johncarlosbaez @OscarCunningham I once had a heated argument with my grade 6 t… |
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Post #Aws7CIW8Anhxy9NAwq by [email protected] |
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@johncarlosbaez The existence of two continued fraction expansions for rational… |
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Post #AwsGbuyxCKfC5p97TM by [email protected] |
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@zwol @MartinEscardo @ccppurcell @maxpool @johncarlosbaez @zwol @MartinEscardo … |
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Post #AwsGbv76i1BYV6xdBI by [email protected] |
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@liuyao - this argument motivates the "Archimedean property", which r… |
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Post #AwsaTUm0kutjZgLyRk by [email protected] |
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@johncarlosbaez @BRicker I was taught a little tiny bit of the tail end of new … |
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Post #Awt11JpOYRa6HXj13w by [email protected] |
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@leon_p_smith @BRicker - sounds good! There's so much to do with math it&#… |
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Post #AwtaftRr2F1mjenTVo by [email protected] |
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@johncarlosbaez @leon_p_smith Strong agree, been saying more people need unders… |
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Post #Awun3D3RhNT6oODyc4 by [email protected] |
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@johncarlosbaez @OscarCunningham maybe you did state this argument already and … |
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Post #Awv7QQwiDOSJdfQUeu by [email protected] |
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@Diffgeometer1 @OscarCunningham - I think @MartinEscardo stated it and @zwol po… |
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Post #AwwgBzZisCuiFWTy7c by [email protected] |
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@johncarlosbaez @OscarCunningham @MartinEscardo @zwol Students doubt algebra? … |
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Post #AwxBEiePLrF3CtSDUu by [email protected] |
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@Diffgeometer1 - should they believe algebra because the teacher said it's … |
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Post #AwxCjcG7GYImJYO9K4 by [email protected] |
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@johncarlosbaez Sadly, most people teaching math are not adequately equipped to… |
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Post #AwxGvvpwhXTQKGH9KC by [email protected] |
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@johncarlosbaez Well, I needed to prove that I could exchange limit and integra… |
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Post #AwxNUgHX7rdRwX8GSe by [email protected] |
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@johncarlosbaezThere's also Fred Richman's approach, based not on the f… |
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Post #AwxRgKVeIg4ni1XqQS by [email protected] |
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@TobyBartels - interesting, thanks! His paper is called "Is 0.999... les… |
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Post #AwxS42iw4w9XUv4DDs by [email protected] |
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@pieter @johncarlosbaez @OscarCunninghamAnyone who thinks the calculator is alw… |
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Post #AwxS42pJhDFzoi3JAW by [email protected] |
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@TobyBartels - and anyone who thinks the teacher is always right, should not be… |
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Post #AwxTKzutrtFLfXJNy4 by [email protected] |
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@johncarlosbaez yes, it’s definitely fine to take different roads in proving … |
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Post #AwxTsrG4ZCN6f2MQsq by [email protected] |
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@Diffgeometer1 wrote: "After explaining why algebra didn’t fail, it’s … |
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Post #AwxhrLI1L2bOa4RYP2 by [email protected] |
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@johncarlosbaez @Diffgeometer1 to be clear, I have not taught entire classes of… |
