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KX21 can't do even the simplest mathPosted by DickT on May 08, 2003 at 06:49:33: In Reply to: M Physics 21: SR's E= SQRT(p^2c^2+ m^2c^4) is an ill-defined function, with more formal Mathematical proof posted by kx21 on May 07, 2003 at 19:47:34:
1) E = sqrt( p^2c^2 + m^2c^4) is a discrete function- It's not discrete but continuous for p >=0, m >=0. The square root function is defined and continuous for those values. 2) the Equation is not a well defined function in the eye of Mathematics... FALSE. As I will show. Given SR:- E = sqrt( p^2c^2 + m^2c^4) iff Here's the problem. There is no justification for "if and only if" (which is what iff means). If would imply that the function f is only defined for the following two cases. NOT SO! F(m,p) = sqrt( p^2c^2 + m^2c^4) is defined for ALL non-negative values of m and p. For p >= 0 and m >= 0. E=mc^2 (m > 0 & p = 0) and E=pc (m = 0 & p > 0). These are the two limiting cases, where either p or m is zero.
f(m,p) =mc^2 (m > 0 & p = 0) =pc (m = 0 & p > 0) = '?' ( m > 0 & p > 0) Kx21's f(m,p) is only defined at p=0 or m=0, and says nothing about the true F(m,p) = sqrt( p^2c^2 + m^2c^4) . You can't prove one function is undefined by talking about some other one. This completes the Proof of both 1) & 2). This shows Kx21's utter bankruptcy in math, but the energy law in SR is triumphant.
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