Description:
Logic -- math, philosophy & computational aspects.
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sciencentechnologies
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Science is a systematic enterprise that builds and organizes knowledge
in the form of testable explanations and predictions about the
universe. In an older and closely related meaning, "science" refers to
the body of reliable knowledge itself, of the type that can be
logically and rationally explained since classical antiquity science... more »
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Matheology § 018
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Feferman and Levy showed that one cannot prove that there is any non-
denumerable set of real numbers which can be well ordered. Moreover,
they also showed that the statement that the set of all real numbers
is the union of a denumerable set of denumerable sets cannot be
refuted.
[Abraham A. Fraenkel, Yehoshua Bar-Hillel, Azriel Levy: "Foundations... more »
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On the definition of Mathematics and its completeness
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In post titled "mathematics is" I had presented a definition of
mathematics, to re-iterate:
Mathematics is the investigation of behaviors that are formalizable in
consistent formal systems extending logic.
Although the concept is correct yet it is immense. There are
infinitely many consistent formal systems that can extend logic, and... more »
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EINSTEIN WRESTLING WITH AN UNSOLVABLE PROBLEM
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[link] John Stachel: "But here he ran into the most blatant-seeming contradiction, which I mentioned earlier when first discussing the two principles. As noted then, the Maxwell-Lorentz equations imply that there exists (at least) one inertial frame in which the speed of light is a constant regardless of the motion of the light source. Einstein's version of the relativity principle (minus the ether) requires that, if this is true for one inertial frame, it must be true for all inertial frames. But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair."... more »
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Matheology § 017
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Matheology § 017
Thesis XIII in Brouwers Dissertation (Appendix): "Over de grondslagen
der wiskunde" (Februari 1907, Dutch) simply reads: "De tweede
getalklasse van Cantor bestaat niet", translated: Cantors second
number class does not exist. {{That is an acceptable foundation of
acceptable mathematics.}}... more »
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Length of a segment with infinitesimal spikes
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This is a variant of a fractal. Suppose we have a ‘smooth’ segment of length 1.
Divide it into n parts, replacing alternate parts by a hat of length m/n. _/\_/\_/\_/\_ . The length of the curve is now (1/2+m/n*n/2) = (m+1)/2.
We let n increase without limit. The height of each spike now goes to 0,... more »
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Matheology § 016
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If we define the real numbers in a strictly formal system, where only
finite derivations and fixed symbols are permitted, then these real
numbers can certainly be enumerated because the formulas and
derivations on the basis of their constructive definition are
countable.
Definiert man die reellen Zahlen in einem streng formalen System, in... more »
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THE SHORTEST REFUTATION OF EINSTEIN'S RELATIVITY
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The observer starts moving towards the light source with speed v so the frequency he measures shifts from f to f' and the speed of light he measures shifts from c to c'. f'=? c'=? [link]
Roger Barlow, Professor of Particle Physics: "Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/(lambda) waves pass a fixed point. A moving point adds another vt/(lambda). So f'=(c+v)/(lambda)."... more »
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Comprehensive Test Banks and solution manuals at good prices
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Comprehensive Test Banks and solution manuals at good prices
Email us at bestsellers.testbanks[at]gmail .com if you need to buy any test bank or solution manual listed below. All emails will be answered quickly. . Test bank and solution manual separately priced. Discounts available if more than 1 item are purchased. All emails will be answered ASAP.... more »
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