formalizing what math assumed as the definition of "finite-number" #439 Correcting Math
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From: Archimedes Plutonium on 16 Feb 2010 17:14 David R Tribble wrote: > Archimedes Plutonium wrote: > > The definition of Real should encompass 10^500 on the leftward string > > and 10^-500 on the rightward string and stop there. So that the > > definition > > of Rational Number is the division of a/b where a and b are from 0 to > > 10^500 and their division is 10^500 or less. > > So a = 10^500/1 is a rational number, and so is b = 1/10^500. > > We would expect, then, that a/b and b/a would also be rational > numbers, right? But of course, according to you, they are not. > > If they are not rational, are they irrational? Or maybe neither? When Finite-number is precisely defined as 10^500 or less, then mathematics is restricted to that realm of finiteness, where Algebra no longer holds true for numbers above or below that realm. So mathematics loses Rational, Irrational, Transcendental, Algebraic. It loses those because multiplication is lost over 90% of all the numbers that exist. Your ideas of Rational numbers was only a quiant naive understanding. The same thing happened in physics when Copernicus, Galileo, Newton showed that Earth is in motion revolving around the Sun, and where guys like you in physics would then have to discard their view of angels flying around the Sun and planets and making them move in epicycles. So David Tribbles ideas of Rational Irrational Transcendental Algebraic were the same as angels making planets move in epicycles. All the Natural Numbers are 0, 1, 2, 3, ........, 9999....9997, 9999....99998, 9999....9999 Multiplication no longer exists for 90% of those numbers. Is the number 9999.....99997 a prime or composite? Impossible to tell because multiplication and division no longer exists after 10000....00000 Is the number 99999....999997 rational or irrational? Impossible to tell because the definition of rational is a repeating block, but that repeating is interfered with by the lone "7" When math gets its act together and defines "finite number" with precision, then math loses its old time messed up and garbled up definitions of Rational, Irrational, Algebraic and Transcendental. Those four were never primary features of mathematics but where homomorphisms placed onto mathematics. Much like saying that the rock cliff looks like a person. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |