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Originally Posted by quanta07 Are these functions contiuous or not continuous..? |
the graph of t1 as ordinate and t2 as abscissa has vertical asymptote at t2=1 and horizontal asymptote at t1 = -1. But the solutions can be restricted to the positive quandrant.
the graph of t2 as ordinate and t1 as abscissa has vertical asymptote at t1 = -1 and horizontal asymptote at t2=1 and again it is practical to limit positive solutions to the positive quandrant.
in any case, neither t1 or t2 ever reaches the exact value of 1 and the simultaneous solution of (0,0) happens if and only if both t1 and t2 are zero. If these are physical quantities then (0,0) is the singularity and can never be reached. Therefore (0,0) becomes the discontinuity between two dimensional levels of existence.
I used this logic in order to create matrices with no zeros elements similar to Hadamard matrices. The products of these square matrices give masses and the sum of these matrices give space charges.
see more about Hadamard matrices at
http://mathworld.wolfram.com/HadamardMatrix.html