Cantor Confusion
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From: MoeBlee on 10 Nov 2006 18:18 Lester Zick wrote: > Your way or the highway huh, Moe(x). If he has an argument that he thinks can be put in set theory, then I'm interested in his argument; If he doesn't think his argument can be put in set theory, then I'm not interested. He can post about his argument all he wants, but I'm not obligated to study his argument. MoeBlee
From: David Marcus on 10 Nov 2006 18:19 Virgil wrote: > WM's problem is that he does not, perhaps cannot, understand that there > is a difference in the way infinite sets and infinite processes work > from the way that finite sets and finite processes work. I think he has a bigger problem. He doesn't seem to agree that there are infinite sets. It is very strange. -- David Marcus
From: Franziska Neugebauer on 10 Nov 2006 18:30 William Hughes wrote: > Franziska Neugebauer wrote: >> William Hughes wrote: >> >> > The length of the set of natural numbers is the supremum of the >> > lengths of the initial segments. >> >> Since when do sets have a length? > > Substitute size or cardinality if you do not like the term > length in this context. It is clear to *me*. Please do me a favor and ask *WM* whether substituting "length" by "cardinality" changes - in his eyes - the subject of your current discussion. F. N. -- xyz
From: Franziska Neugebauer on 10 Nov 2006 18:30 David Marcus wrote: > Franziska Neugebauer wrote: >> David Marcus wrote: >> >> > [...] you are working with an infinite triangle [...] >> >> ,----[ http://en.wikipedia.org/wiki/Triangle ] >> | A triangle is one of the basic shapes of geometry: a polygon with >> | three vertices [...] >> `---- >> >> Are there really three vertices in WM's "triangle"? > > No. But, I don't think an "infinite triangle" needs to be a triangle. > However, I'm open to suggestions for what to call it. I would prefer discussions either with precisely defined (formalized) "infinite triangles" or better without all these words borrowed from Cantor/geometry/physics. F. N. -- xyz
From: Virgil on 10 Nov 2006 18:43
In article <1163180572.015523.176260(a)e3g2000cwe.googlegroups.com>, mueckenh(a)rz.fh-augsburg.de wrote: > Virgil schrieb: > > > > > Why don't you try to find out how it could be presented in set theory? > > > Or why that cannot be done? > > > > We have already seen why it cannot be done in ZF or NBG. It contradicts > > the requirements of those systems. > > > > > > You have seen nothing but the fact that it contradicts the *results* of > those systems. > > Regards, WM They are parts of the system. WM's claims violate ZF. ZFC. NBG, and others without even having a completely stated set of assumptions. Absent statement of a complete set of assumptions or rules, WM's "system" is not even a system, but a game being played without rules. Such unruly games are too uncertain for the needs of mathematics. |