Description:
Mathematical discussions and pursuits.
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S orthonormal -> S countable
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Suppose X is a separable space endowed with an inner product. Is S is a set of orthonormal vectors in X, it is finite or countably infinite. The argument points out that if u,v belong to S then ||u-v||^2=2 so the elements of S are at a certain positive distance from one another. It then procedes to show that the number of spheres with centers in the... more »
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Symmetry and homogeneity.
 
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...Tom: <Then in GR you must include the mechanism of deformation in the energy-momentum tensor. That gives you a completely different problem to study, and it's not obvious how to compare two such different situations....> In the LTE of SR the mechanism was spelled out by Lorentz in his 1904 paper.... more »
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Cardinality of proper classes:
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Hi all, Is there a definition of Cardinality of proper classes. I know of one example were that can be defined, and that is when we have global choice, so in MK\NBG with Global choice, we can define Cardinality in usual manner using Von Neumann Cardinals. However what about defining Cardinality of proper classes when we... more »
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Help sought: Does anyone recognize this series in physical systems?
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Help sought: Does anyone recognize this series in physical systems? ------------------------------ ------------------------------ ------- Interesting little pattern spotted. 2 x (1) 2 x (2x1, 2x3) 2 x (2x1, 2x5, 2x3) 2 x (2x1, 2x7, 2x5, 2x3) The convention is that the first column doubles what is to the right... more »
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n! > n^2 for every integer n >= 4
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I want to show by the principle of mathematical induction that n! > n^2 for every integer n >= 4. However, I am unable to do the induction step correctly. That is, I am unable to show that (n + 1)! > (n + 1)^2 when n! > n^2. Could someone please help me?
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A Mathematical Term for Everything
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We can put a person on the moon but we cannot define the trajectory of the rocket that takes him there. How is it that we can build skyscrapers that seem to defy gravity yet the slope of their vertical walls is undefined? The answer to a math problem should never be “undefined”. Why didn’t they just define it?... more »
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help with complex function
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I have to solve the following problem; I have a complex function f(w) f(w) = 1 + exp(i*a*w) + exp(i*b*w) where a and b are coefficients and i = sqrt(-1) For a given value of w (= w0), I am interested in finding the values of a and b that cause f(w) to become 0. Of course there are infinitely many combinations of a and b that can satisfy this condition, but I am... more »
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