Re: Language feature selection

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From	Paul Rubin <no.email@nospam.invalid>
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Subject	Re: Language feature selection
Date	Fri, 17 Mar 2017 11:03:09 -0700
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Tom Gardner <spamjunk@blueyonder.co.uk> writes:
> It was sufficient for us to believe in the concepts, and to be able to
> understand the explanation of how polynomials (except 1/x) could be
> differentiated. 

I think that might have been a less rigorous treatment than is usually
seen in calculus classes where students get confused by limits.  

Here's a cute problem that can let you check your understanding.  It's
about continuity rather than limits per se, but if you understand one
you probably understand the other.

Consider the function f(x) defined as follows:

  if x is a rational number p/q in lowest terms, then f(x) = 1/q.

  if x is irrational, then f(x) = 0.

Questions: 

  1) For what values of x, if any, is f(x) continuous?

  2) For what values of x, if any, is f(x) discontinuous?

Thread

Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-05 16:03 -0700
  Re: Language feature selection Wouter van Ooijen <wouter@voti.nl> - 2017-03-06 08:04 +0100
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-07 10:31 -0700
      Re: Language feature selection Wouter van Ooijen <wouter@voti.nl> - 2017-03-07 23:29 +0100
        Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-08 02:49 -0700
          Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-08 13:18 +0100
            Re: Language feature selection Wouter van Ooijen <wouter@voti.nl> - 2017-03-08 16:58 +0100
            Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-08 10:35 -0700
              Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-08 22:07 +0100
  Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-06 08:40 +0100
    Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-06 10:31 +0100
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-06 08:47 -0700
      Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-06 21:33 +0100
        Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-06 13:44 -0700
          Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-07 12:24 +0100
            Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-07 09:34 -0700
              Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-08 10:14 +0100
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-08 10:37 -0700
                Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-08 22:09 +0100
    Re: Language feature selection Tauno Voipio <tauno.voipio@notused.fi.invalid> - 2017-03-06 22:50 +0200
      Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-07 12:31 +0100
    Re: Language feature selection rickman <gnuarm@gmail.com> - 2017-03-07 14:45 -0500
  Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-06 08:39 +0000
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-06 08:39 -0700
      Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-06 17:27 +0000
        Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-06 13:30 -0700
  Re: Language feature selection Dimiter_Popoff <dp@tgi-sci.com> - 2017-03-06 11:11 +0200
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-06 13:38 -0700
      Re: Language feature selection Dimiter_Popoff <dp@tgi-sci.com> - 2017-03-07 12:18 +0200
        Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-07 10:28 -0700
  Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-06 13:33 -0500
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-06 13:36 -0700
      Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-06 22:15 -0500
        Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-06 22:22 -0500
        Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-07 00:27 -0700
          Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-08 12:20 -0500
            Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-08 11:23 -0700
              Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-10 13:43 -0500
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-10 16:49 -0700
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-11 04:17 -0500
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-11 12:33 -0700
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-12 18:08 -0400
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-12 17:25 -0700
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-15 21:05 -0400
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-16 17:23 -0700
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-17 23:59 -0400
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-17 23:25 -0700
                Re: Language feature selection Tauno Voipio <tauno.voipio@notused.fi.invalid> - 2017-03-18 12:05 +0200
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-18 04:04 -0700
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-18 04:39 -0700
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-18 03:55 -0700
                Re: Language feature selection upsidedown@downunder.com - 2017-03-18 16:00 +0200
                Re: Language feature selection Les Cargill <lcargill99@comcast.com> - 2017-03-11 16:35 -0600
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-11 15:39 -0700
  Re: Language feature selection Grant Edwards <invalid@invalid.invalid> - 2017-03-06 18:59 +0000
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-06 12:36 -0700
  Re: Language feature selection Simon Clubley <clubley@remove_me.eisner.decus.org-Earth.UFP> - 2017-03-07 19:02 +0000
    Re: Language feature selection Grant Edwards <invalid@invalid.invalid> - 2017-03-07 19:18 +0000
      Re: Language feature selection Grant Edwards <invalid@invalid.invalid> - 2017-03-07 19:19 +0000
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-07 12:38 -0700
  Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-07 22:10 -0600
    Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-07 20:35 -0800
      Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-08 20:43 -0600
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-07 23:48 -0700
      Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-08 20:48 -0600
        Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-08 21:15 -0700
        Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-09 01:33 -0800
        Re: Language feature selection Grant Edwards <invalid@invalid.invalid> - 2017-03-09 14:47 +0000
          Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-09 16:40 +0100
            Re: Language feature selection Grant Edwards <invalid@invalid.invalid> - 2017-03-09 16:15 +0000
              Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-09 22:04 +0100
                Re: Language feature selection John Devereux <john@devereux.me.uk> - 2017-03-10 07:46 +0000
                Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-10 13:21 +0100
              Re: Language feature selection Les Cargill <lcargill99@comcast.com> - 2017-03-09 17:57 -0600
                Re: Language feature selection Tauno Voipio <tauno.voipio@notused.fi.invalid> - 2017-03-10 11:16 +0200
        Re: Language feature selection Jacob Sparre Andersen <jacob@jacob-sparre.dk> - 2017-03-10 20:39 +0100
          Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-10 13:32 -0800
            Re: Language feature selection Niklas Holsti <niklas.holsti@tidorum.invalid> - 2017-03-11 14:58 +0200
              Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-13 13:02 +0100
    Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-08 10:46 +0100
      Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-08 20:33 -0600
        Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-09 11:08 +0100
          Re: Language feature selection Britt <britt.snodgrass@gmail.com> - 2017-03-09 07:04 -0800
            Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-09 16:36 +0100
              Re: Language feature selection Grant Edwards <invalid@invalid.invalid> - 2017-03-09 16:11 +0000
              Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-09 12:06 -0600
              Re: Language feature selection Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2017-03-09 19:26 +0100
                Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-09 22:08 +0100
            Re: Language feature selection Simon Clubley <clubley@remove_me.eisner.decus.org-Earth.UFP> - 2017-03-09 19:04 +0000
              Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-09 15:34 -0700
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-09 15:40 -0700
                Re: Language feature selection Simon Clubley <clubley@remove_me.eisner.decus.org-Earth.UFP> - 2017-03-10 14:19 +0000
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-10 11:10 -0700
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-10 11:49 -0700
        Re: Language feature selection Les Cargill <lcargill99@comcast.com> - 2017-03-09 18:00 -0600
    Re: Language feature selection Les Cargill <lcargill99@comcast.com> - 2017-03-09 17:54 -0600
      Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-09 18:54 -0600
        Re: Language feature selection Grant Edwards <invalid@invalid.invalid> - 2017-03-10 04:07 +0000
          Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-10 08:07 -0600
        Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-10 13:59 +0100
      Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-10 08:17 +0000
        Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-10 11:24 -0700
          Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-10 19:09 +0000
            Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-10 12:33 -0700
              Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-10 23:25 +0000
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-10 20:22 -0500
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 01:32 +0000
                Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-10 18:16 -0800
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 09:59 +0000
                Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-11 02:23 -0800
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 11:13 +0000
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-11 14:28 -0500
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-11 17:20 -0500
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-12 16:26 -0400
                Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-12 21:46 +0100
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-12 23:15 +0000
                Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-13 14:14 -0400
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-13 18:48 +0000
                Re: Language feature selection "Brian G. Lucas" <bagel99@gmail.com> - 2017-03-13 15:17 -0500
                Re: Language feature selection Niklas Holsti <niklas.holsti@tidorum.invalid> - 2017-03-13 23:17 +0200
                Re: Language feature selection "Brian G. Lucas" <bagel99@gmail.com> - 2017-03-13 17:27 -0500
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-13 17:10 -0700
                Re: Language feature selection Niklas Holsti <niklas.holsti@tidorum.invalid> - 2017-03-14 10:11 +0200
                Re: Language feature selection "Brian G. Lucas" <bagel99@gmail.com> - 2017-03-14 12:23 -0500
                Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-14 13:27 +0100
                Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-14 13:30 -0400
                Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-14 22:03 +0100
                Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-14 17:24 -0400
                Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-11 07:19 -0600
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 19:43 +0000
                Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-12 09:28 -0600
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-12 15:15 -0400
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-12 19:38 +0000
                Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-10 18:08 -0800
                Re: Language feature selection George Neuner <gneuner2@comcast.net> - 2017-03-11 04:22 -0500
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 10:02 +0000
                Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-11 02:22 -0800
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 11:07 +0000
          Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-10 14:30 -0600
            Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-10 13:37 -0800
              Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-10 16:30 -0600
                Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-10 18:14 -0800
                Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-11 07:46 -0600
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-11 12:53 -0700
                Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-12 09:45 -0600
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-12 11:56 -0700
                Re: Language feature selection Dimiter_Popoff <dp@tgi-sci.com> - 2017-03-12 21:05 +0200
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-12 14:40 -0700
                Re: Language feature selection Dimiter_Popoff <dp@tgi-sci.com> - 2017-03-13 00:36 +0200
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-12 17:00 -0700
                Re: Language feature selection Robert Wessel <robertwessel2@yahoo.com> - 2017-03-13 16:50 -0500
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-13 17:08 -0700
                Re: Language feature selection Robert Wessel <robertwessel2@yahoo.com> - 2017-03-13 20:51 -0500
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-13 20:31 -0700
                Re: Language feature selection Robert Wessel <robertwessel2@yahoo.com> - 2017-03-14 21:45 -0500
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-14 21:16 -0700
                Re: Language feature selection Les Cargill <lcargill99@comcast.com> - 2017-03-11 16:40 -0600
            Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-10 15:10 -0700
              Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-10 16:42 -0600
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-10 17:02 -0700
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 00:46 +0000
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-11 13:05 -0700
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 21:58 +0000
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-11 15:19 -0700
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-11 23:27 +0000
                Re: Language feature selection Walter Banks <walter@bytecraft.com> - 2017-03-10 20:14 -0600
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-11 12:16 -0700
        Re: Language feature selection Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2017-03-10 20:40 +0100
          Re: Language feature selection Wouter van Ooijen <wouter@voti.nl> - 2017-03-10 22:28 +0100
  Re: Language feature selection Jacob Sparre Andersen <jacob@jacob-sparre.dk> - 2017-03-10 20:03 +0100
    Re: Language feature selection Grant Edwards <invalid@invalid.invalid> - 2017-03-10 19:48 +0000
      Re: Language feature selection Jacob Sparre Andersen <jacob@jacob-sparre.dk> - 2017-03-13 21:25 +0100
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-10 13:03 -0700
      Re: Language feature selection Jacob Sparre Andersen <jacob@jacob-sparre.dk> - 2017-03-13 21:40 +0100
        Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-13 14:35 -0700
          Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-14 01:06 +0000
            Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-13 19:23 -0700
              Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-14 08:48 +0000
                Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-14 02:14 -0700
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-14 09:33 +0000
                Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-14 09:21 -0700
                Re: Language feature selection Les Cargill <lcargill99@comcast.com> - 2017-03-17 06:01 -0500
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-17 11:39 +0000
                Re: Language feature selection Les Cargill <lcargill99@comcast.com> - 2017-03-17 07:16 -0500
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-17 13:49 +0000
                Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-17 11:03 -0700
                Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-17 19:21 +0100
                Re: Language feature selection Paul Rubin <no.email@nospam.invalid> - 2017-03-17 11:34 -0700
                Re: Language feature selection David Brown <david.brown@hesbynett.no> - 2017-03-17 20:26 +0100
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-17 20:07 +0000
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-17 20:29 +0000
                Re: Language feature selection Les Cargill <lcargill99@comcast.com> - 2017-03-17 19:19 -0500
                Re: Language feature selection Tom Gardner <spamjunk@blueyonder.co.uk> - 2017-03-18 08:18 +0000
            Re: Language feature selection Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2017-03-14 21:20 +0100
  Re: Language feature selection jim.brakefield@ieee.org - 2017-03-10 18:46 -0800
    Re: Language feature selection Niklas Holsti <niklas.holsti@tidorum.invalid> - 2017-03-11 15:41 +0200
      Re: Language feature selection jim.brakefield@ieee.org - 2017-03-11 14:20 -0800
        Re: Language feature selection upsidedown@downunder.com - 2017-03-12 00:54 +0200
          Re: Language feature selection jim.brakefield@ieee.org - 2017-03-12 18:08 -0700
            Re: Language feature selection upsidedown@downunder.com - 2017-03-13 23:36 +0200
          Re: Language feature selection Robert Wessel <robertwessel2@yahoo.com> - 2017-03-13 17:03 -0500
    Re: Language feature selection Don Y <blockedofcourse@foo.invalid> - 2017-03-11 14:21 -0700

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