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Originally Posted by The_Liquid_Laser
Heh mathematics is so vast I wonder how many topics will be brought up that most of the rest of us are not familiar with. For example I don't think I've ever encountered Gaussians (or if I have, then I have forgotten).
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I'm sure you've come across them.
Gaussians are often called "normal distributions" (though I usually reserve this for the mean=0, std. dev.=1 Gausssian of 1 dimension) or "the bell-curve."
Gauss may is one of the greatest mathematicians to ever live (Euclid and Euler may be the only ones more influential). So I like calling the curves Gaussians.
Quote:
Originally Posted by The_Liquid_Laser
Here are some things off the top of my head that I find interesting:
*Formally I believe that a set is defined to have cardinality Aleph1 if its cardinality is equivalent to the cardinality of the power set of Aleph0. I have seen it mentioned that the cardinality of the real numbers is Aleph1, but I don't think this has been proven. (Or if it has been proven I would like to know.)
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This wikipedia article covers the
Continuum hypothesis fairly well
Quote:
Originally Posted by The_Liquid_Laser
*I find terms like real, irrational, and imaginary to be amusing. For example the real numbers have some features that seem unrealistic. Both the rationals and irrationals are dense within the real numbers, but the rationals have the same cardinality as the natural numbers, while the irrationals have the same cardinality as the real numbers.
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I always found these things pretty cool. There was a puzzle about getting out of hell some day by guessing the
pair of numbers the devil was thinking about. It's rather simple, but it proved that this set (a pair of integers) is countable (and therefore had the same cardinality as the numbers used to count) . Of course, it is a short hop to rationals being countable.
The matching of real-numbers to irrationals is a bit less obvious, but the cut
Dedekind cut formulation of rational numbers seems to make it pretty clear.
The "real" numbers have quite a bit more application that the integers or rationals, since most sciences assume a continuum (at least at mid to large scales).
Quote:
Originally Posted by The_Liquid_Laser
*Fractals - I just think they are neat. They represent well ordered chaos to me.
*I've seen a hypercube which is an abstraction of a forth dimensional object, but I'd like to see more elaborate forth dimensional representations.
*I've found Flatlands to be an interesting book. It is a simple fictional book about how a three dimensional person would interact in a two dimensional world. It is implied that one can extrapolate how a forth dimensional object would be observed by three dimensional people.
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Keith Devlin should be name "math evangelist of the decade," imo. Your list seems like a list of the books he's written.
