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Posted by Mark on September 18, 2001 19:16:44 UTC

>>>>Of course, the paradox to that supposition is that if everything is mathematical then how is that we are able to lie and make mathematical errors when we do math. That is, what allows us the freedom from mathematical order so that we are not so connected to the 'math world' that we actually cause a clear contradiction to that order? to a < or the + to a -, the statement becomes plausible. There are a multitude of changes I could make to cure the equation of its "paradoxical flu"..... I could change the 4 to a 13, or change one of the 5's to a -7..... instead of a comma between a & b I could replace it with the word "or". Did I lie on behalf of my own free will?, or did I mistakingly throw symbols about that are understood to have a particular meaning which negates the possibility of the above statement having a "true solution".
What if you came along and gave an ad hoc resolution to the above paradox by giving this as your as possible values for a & b, "Within the complex number system, the possible values for a & b are given by the empty set: { }.... that's not to say that there are no possible solutions in some other number system, if I get to play "creator" over the algabraic rules and opperations within the set."
This new "set" would be superalgabraic, just like the sqrt of -1 is not contained within the set of real numbers. We created a "super-real" set that contains the real numbers as a subset; this set is just the complex numbers, and contained within it is the solution to sqrt -1, formaly known as i.

Is all this even what you were talking about?

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