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Raising a number to a non-integer power.

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hamster_nz:

--- Quote from: T3sl4co1l on June 03, 2020, 11:51:51 pm ---One of the few truly real, non-computable numbers that we can even begin to grasp, is: https://en.wikipedia.org/wiki/Chaitin%27s_constant

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Thanks for that Wikipedia wormhole  :)... I've never heard of it till now.

magic:

--- Quote from: T3sl4co1l on June 03, 2020, 11:51:51 pm ---Now consider that, for as many numbers as a googolplex, there are far more numbers than that, just among the rationals between 0 and 1; but compared to the number of uncomputable reals in the same range, even that infinity has measure zero, and not just laughably so, but trivially so!

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Screw computability; most irrationals can't even be individually described and identified by any finite text or formula in any language in existence. Some people got quite upset when one Cantor raised this issue some 150 years ago ;D

You can have sets of real numbers which can't be assigned any length/area/volume because every possible value from zero to infinity leads to one or another paradox. And many mathematicians will tell you with a straight face that from a few such unmeasurable sets in a 3D space it is possible to assemble various measurable sets of different volumes just by moving and rotating them around. Some others feel a bit uneasy about that idea, though.

CatalinaWOW:
There is so much esoterica in advanced mathematics.  I find it challenging enough to understand and use the crumbs that very bright people pull out of that heap and show the real world applications to us mere mortals.  Distributions, contour integrals and a whole list of other tools.  But those people are made to pay for their sins.  In grad school I took several advanced mathematics courses in aid of understanding the limits and applications of those crumbs.  The courses were owned and taught be the mathematics department.  But 80-90% populated by engineers and physicists.  Which irked the mathematicians no end.  And caused immense disdain for their colleagues who continued finding and disseminating those crumbs.

T3sl4co1l:


Tim

CatalinaWOW:
Very good opening.

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