geometry precisely defining ellipsis and how infinity is in the midsection #426 Correcting Math
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From: Archimedes Plutonium on 13 Feb 2010 02:17 Archimedes Plutonium, on Jan 27, 2010 2:41 AM, wrote: --- old post of Jan 27 --- One can say the trick of Euclid's infinitude of primes proof is to "multiply the lot and add 1". I prefer to call it the mechanism of the proof rather than the slimey (sic) connotation of "trick." But maybe I have found a trick or mechanism to get me that clarity I seek above. Consider this line-ray: ----------------------------------------> Can I play a trick in the proof by saying that line-ray has to yield all the line-segments and line-rays? Then, can I say that the above line-ray can be put into a correspondence of the largest line-ray with the largest line-segment? The largest line-ray is the above line-ray itself. Now the largest line-segment, and what is that? Does there have to be a largest line-segment? Can it be infinitely long, and of course not for it must have a second endpoint. Must it exist? Yes of course it must exist in that it has two endpoints and it cannot be an infinite-ray. So here is a forced Selection. In that we are required to correspond the largest line-ray since we do have a largest line-ray, and so, we must have a largest line-segment. Hence, we must Pick and Chose and Select a line-segment and call it the boundary between Finite and Infinite-line. Yes, I am getting happy and gratified. The idea is that there is obviously a largest Line-ray and that forces me to find the largest line-segment to match with the largest line-ray. If there is no largest line-segment means that there is a line segment which is the same as a line-ray. Contradiction. P.S. I could not do this proof for Peano Natural Numbers because finite-number and infinite number were never given a precision definition, unlike geometry. So this proof is do-able because in geometry we have a precision definition of finite-line versus infinite-line. --- old post of Jan 27 --- What I am doing now is deriving a precise definition of ellipsis and showing that the precision definition in geometry of a finite-line versus infinite- line is able to not only prove a Selection process has to take place in Numbers for a precision definition but that the geometry can define "ellipsis" and also help to understand that a number can have a FrontView with BackView and where the "infinity is in the middle section of the number." All of this is able to be done because Geometry, in all of its history had a precision definition of finite line (line-segment) versus infinite- line (line-ray). Because Geometry had that precision all along, that Numbers can just borrow that precision and give a precise definition of finite-number versus infinite-number, but it also affords a precision definition of ellipsis as well as the understanding that a number can and must have a FrontView with BackView and where infinity is in the middle section of the number. Three cheers to geometry. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |