The Definition of Points
in [Math]
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From: Mike Kelly on 1 Apr 2007 07:06 On 1 Apr, 04:44, Tony Orlow <t...(a)lightlink.com> wrote: > cbr...(a)cbrownsystems.com wrote: > > On Mar 31, 5:45 pm, Tony Orlow <t...(a)lightlink.com> wrote:> > >> Yes, NeN, as Ross says. I understand what he means, but you don't. > > > What I don't understand is what name you would like to give to the set > > {n : n e N and n <> N}. M? > > > Cheers - Chas > > N-1? Why do I need to define that uselessness? I don't want to give a > size to the set of finite naturals because defining the size of that set > is inherently self-contradictory, So.. you accept that the set of naturals exists? But you don't accept that it can have a "size". Is it acceptable for it to have a "bijectibility class"? Or is that taboo in your mind, too? If nobody ever refered to cardinality as "size" but always said "bijectibility class" (or just "cardinality"..) would all your objections disappear? > given the fact that its size must be equal to the largest element, That isn't a fact. It's true that the size of a set of naturals of the form {1,2,3,...,n} is n. But N isn't a set of that form. Is it? -- mike.
From: Bob Kolker on 1 Apr 2007 07:10 Tony Orlow wrote: > > Except that linear order (trichotomy) and continuity are inherent in R. > Those may be considered geometric properties. They are -order- properties. Your choice to picture them geometrically is an arbitrary decision on your part. One can deal with complete orderings without a scintilla of geometry. Bob Kolker
From: Bob Kolker on 1 Apr 2007 07:11 T. O wrote. > One may express them algebraically, but their truth is derived and > justified geometrically. There is only one justification in mathematics. Does the conclusion follow logically from the premises. Bob Kolker
From: Bob Kolker on 1 Apr 2007 07:12 Tony Orlow wrote:> > That is like saying your mind has outgrown your body, so you no longer > need to eat or breathe. The language of math is the more abstract > aspect, but the geometry of it is still the basis of its truth. So it counting. Bob Kolker
From: Bob Kolker on 1 Apr 2007 07:12
Tony Orlow wrote: > > That is like saying your mind has outgrown your body, so you no longer > need to eat or breathe. The language of math is the more abstract > aspect, but the geometry of it is still the basis of its truth. So is counting. Bob Kolker |