Cantor Confusion
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From: Han de Bruijn on 27 Oct 2006 03:25 mueckenh(a)rz.fh-augsburg.de wrote: > [ ... snip ... ] By the way, the first draft of my website > on MatheRealism is ready including links to your site. > > http://www.fh-augsburg.de/~mueckenh/MR.mht I've seen it. Very good! Han de Bruijn
From: Han de Bruijn on 27 Oct 2006 03:38 David Marcus wrote: > Please name the mathematicians that agree that your argument is correct. > (Han doesn't count, since he says he is a physicist.) A Theoretical Physicist. Mathematical Physics and Physical Mathematics. Han de Bruijn
From: Han de Bruijn on 27 Oct 2006 03:53 Virgil wrote: > In article <1161884380.178413.126960(a)i3g2000cwc.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: > >>David Marcus schrieb: >> >>>>All the balls have been removed before noon. >>> >>>OK. >>> >>>>But more balls are in the vase. >>> >>>Reason? Proof? Example? Anything? >> >>Consider a strictly increasing sequence with non-negative >>terms.--------- If you can. > > Consider that the number of balls as a function of time has infinitely > many integer jump discontinuities which cluster around noon, so that > there is no way that the function can be continuous at noon. Huh! Consider the Ocean as defined by Tony Orlow. Replace the balls in a vase by the water molecules in an ocean - what hell is the difference!? Then use a continuous model, as is _routinely done_ with Fluid Dynamics. And there IS a way that the function can be continuous at noon. But the problem is that you mathematicians do not understand what continuity IS. You cannot comprehend that there can be a discrete as well as continuous description for one and the same (physical) phenomenon. See for example the Fluid Tube Continuum: http://hdebruijn.soo.dto.tudelft.nl/QED/index.htm#ft Han de Bruijn
From: Sebastian Holzmann on 27 Oct 2006 06:31 Virgil <virgil(a)comcast.net> wrote: > In article <1161883732.413718.244570(a)k70g2000cwa.googlegroups.com>, > mueckenh(a)rz.fh-augsburg.de wrote: >> What you propose, namely the infinity of ZF without the axiom INF would >> not be an advance. But meanwhile you may have recognized that your >> assertion (ZF even without INF is not finite) is false. > > It is, however, quite true that ZF without INF need not be finite. It is, more than that, quite true that ZF without INF _is_ infinite (the axiom schema of separation alone provides infinitely many axioms). The point is: ZF without INF does not prohibit the existence of infinite sets, nor does it force them to exist.
From: Sebastian Holzmann on 27 Oct 2006 06:33
mueckenh(a)rz.fh-augsburg.de <mueckenh(a)rz.fh-augsburg.de> wrote: > > Sebastian Holzmann schrieb: > What you regard as foolish is the explanation of the axioms which seem > to be your gospel. These axioms and their meaning have not yet changed > (as far as I know from modern text books and from the internet page of > T. Jech (a leading set theorist of our days)). Which modern text book have you read? I cannot find any non-biographical texts on Jech's internet page. Please do elaborate (or rather: please don't...) |