Rational numbers whose decimal representations have a finite length are well-ordered. In third grade they divide integers. This may lead to rational quotients but they just write 34R3, for example, if the remainder is 3.
--- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Fri, Apr 30, 2021, 12:01 PM jon zingale <[email protected]> wrote: > Mmm, long division is an interesting one. Who am I to say how things must > be proved, but the proofs of the division algorithm with which I am > familiar involve the well-ordering principle. There, in this one idea, lies > two problematic details: > > 1. The non-algebraic nature of the well-ordering principle > <https://en.wikipedia.org/wiki/Well-ordering_principle>, and its > correlative controversies. As outlined in the paper, "It has been shown > that if you want to believe the well-ordering theorem, then it must be > taken as an axiom." > > 2. The first significant moment where intension in the form of > computational complexity enters an otherwise extensional number theory. > ------------------------------ > Sent from the Friam mailing list archive > <http://friam.471366.n2.nabble.com/> at Nabble.com. > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: http://friam.471366.n2.nabble.com/ >
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