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Re: ds^2 and metric tensor

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Użytkownik "JanPB"  napisał w wiadomości grup 
dyskusyjnych:42b3857f-9843-4954-afa3-964e45541b86@googlegroups.com...

On Friday, November 18, 2016 at 5:12:38 AM UTC-8, mlwo...@wp.pl wrote:
> A question for both these mumbling halfbrains
> pretending gurus here:
> So , ds^2 in the formula ds^2= dx^2/x^4 + dy^2
> is a metric tensor, right?
> If it is, dx^2/x^4 +dy^2 must be a formula giving
> a real number scalar. Is it really?

|It gives a real number if you plug in a pair of tangent vectors (say, u and 
v)
|at a point (say (x,y)) into ds^2. Let's do that, for example consider these
|u and v:

|  ds^2|_(x,y)(u,v) = (1*3)/(4^4) + 2*(-7) = 3/256 - 14 = -3581/256


So,  poor idiot, we have:
1)ds^2
2)ds^2|_(x,y)(u,v)
You're a true idiot, but I think you can still notice some difference,
can't you?
Which one gives a real number? The second one, right?
And the second one  is your tensor.
1) is a square of differential. Of course, you don't know what
it means, but I write for others, not for you.

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ds^2 and metric tensor mlwozniak@wp.pl - 2016-11-18 05:12 -0800
  Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-18 12:26 -0800
    Re: ds^2 and metric tensor Hank Barco <hankbarco@hankbarco.org> - 2016-11-18 21:05 +0000
    Re: ds^2 and metric tensor Maciej Woźniak <mlwozniak@wp.pl> - 2016-11-19 10:04 +0100
      Re: ds^2 and metric tensor paparios <paparios@gmail.com> - 2016-11-19 05:56 -0800
        Re: ds^2 and metric tensor Maciej Woźniak <mlwozniak@wp.pl> - 2016-11-19 15:24 +0100
        Re: ds^2 and metric tensor Gary Harnagel <hitlong@yahoo.com> - 2016-11-19 06:30 -0800
      Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-19 15:55 -0800
        Re: ds^2 and metric tensor Maciej Woźniak <mlwozniak@wp.pl> - 2016-11-20 08:49 +0100
          Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-20 01:35 -0800
            Re: ds^2 and metric tensor Maciej Woźniak <mlwozniak@wp.pl> - 2016-11-20 14:17 +0100
              Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-20 20:38 -0800
                Re: ds^2 and metric tensor mlwozniak@wp.pl - 2016-11-20 22:54 -0800
                Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-20 23:08 -0800
                Re: ds^2 and metric tensor Maciej Woźniak <mlwozniak@wp.pl> - 2016-11-21 21:45 +0100
                Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-21 13:17 -0800
                Re: ds^2 and metric tensor Tom Roberts <tjroberts137@sbcglobal.net> - 2016-11-21 16:17 -0600
                Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-21 16:15 -0800
                Re: ds^2 and metric tensor mlwozniak@wp.pl - 2016-11-21 23:31 -0800
                Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-22 00:36 -0800
                Re: ds^2 and metric tensor mlwozniak@wp.pl - 2016-11-22 01:53 -0800
                Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-22 14:06 -0800
                Re: ds^2 and metric tensor alsor@interia.pl - 2016-11-22 14:31 -0800
                Re: ds^2 and metric tensor "David (Lord Kronos) Fuller" <fuller.david@hotmail.com> - 2016-11-22 14:42 -0800
                Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-22 15:41 -0800
                Re: ds^2 and metric tensor alsor@interia.pl - 2016-11-24 12:50 -0800
                Re: ds^2 and metric tensor mlwozniak@wp.pl - 2016-11-22 23:18 -0800
                Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-22 23:49 -0800
                Re: ds^2 and metric tensor mlwozniak@wp.pl - 2016-11-23 02:34 -0800
                Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-23 14:58 -0800
                Re: ds^2 and metric tensor mlwozniak@wp.pl - 2016-11-23 23:31 -0800
        Re: ds^2 and metric tensor alsor@interia.pl - 2016-11-20 08:17 -0800
          Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-20 20:45 -0800
            Re: ds^2 and metric tensor alsor@interia.pl - 2016-11-22 11:45 -0800
              Re: ds^2 and metric tensor JanPB <filmart@gmail.com> - 2016-11-23 16:38 -0800
                Re: ds^2 and metric tensor alsor@interia.pl - 2016-11-24 12:56 -0800
  Re: ds^2 and metric tensor alsor@interia.pl - 2016-11-19 09:15 -0800
    Re: ds^2 and metric tensor Norberto Haman <norberman@norberman.info> - 2016-11-19 17:25 +0000
      Re: ds^2 and metric tensor alsor@interia.pl - 2016-11-19 11:21 -0800

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