Virgil
Posts:
7,034
Registered:
1/6/11


Re: Matheology � 295
Posted:
Jun 26, 2013 5:24 PM


In article <19316c5e87af4d00acb6e0bcde79850a@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Tuesday, 25 June 2013 02:03:36 UTC+2, Zeit Geist wrote: > > On Monday, June 24, 2013 2:04:19 PM UTC7, muec...@rz.fhaugsburg.de wrote: > > > > > On Monday, June 24, 2013 2:04:19 PM UTC7, muec...@rz.fhaugsburg.de wrote: > > On Monday, 24 June 2013 20:51:15 UTC+2, Zeit Geist wrote: > > > > > The use of oo shows your nativity. > > We're discussing Ordinals and Cardinals not real numbers. > > 1/aleph_0 is meaningless. > > So we have a new theorem of independence? aleph_0 is independent of the > natural numbers.
WRONG! AGAIN!! AS USUAL!!!
Aleph_0 is not a member of the set of natural numbers but is the cardinality of that set. > > No, cardinals are numbers, because they are in trichotomy with natural > numbers and with each other.
Trichotomy is a property of linearly ordered sets, including those whose members are not numbers.
The set of all FISONs, for example. is linearlyordered (and wellordered) by inclusion, and satisfies trichotomy, even though FISONs are not numbers.
WM's immense ignorance of honest mathematics is again revealed.
> It cardinals were not numbers, they could not be > of any use in mathematics.
Are quaternions "numbers"? Are matrices numbers? Are vector spaces numbers? There are a lot of things in the mathmatics outside of WMytheology which are not numbers but are still quite useful in mathemaics.
> > 1/aleph_0 < 1 In which number system is this supposed to hold?
In order to have an order relation, one must specify the set of objects which are comparable with that order relation.
WM has not given us that set nor defined that relation on that set.
> 1/{ } > 100
Only in WM's wild weird world of WMytheology > > >> ZFC is the foundation of mathematics. > >> Mathematics has the axiom of trichotomy.
Nonsense! A total order relations on a set has trichotomy, but there is no such "axiom of trichotomy" for all of mathematics, if for no other reason that not all sets have one and only one totally ordering.
> Unnameable numbers cannot be put in trichotomy.
At least not by WM.
Can triangles be put into some sort of unique trichotomy? Note that would require all triangles that come out "equal" to be just one triangle. > >> Contradiction. >
> That's a very good question for klein Haenschen. You are not mathematician > enough to understand that with ten labels you cannot label 100 objects?
Actually, with only 10 labels, like 0,1,2,3,4,5,6,7,8 and 9, for instance, any competent mathematician can label any finite number different objects with different labels.
A real mathematician can even do it with only two labels. 

