Re: Question


Arturo Magidin wrote:
In article <1146070084.348399.269880@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
zuhair <zaljohar@xxxxxxxxx> wrote:

Arturo Magidin wrote:
In article <1145996666.531448.45830@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
zuhair <zaljohar@xxxxxxxxx> wrote:

Virgil wrote:
In article <1145991892.167851.295010@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"zuhair" <zaljohar@xxxxxxxxx> wrote:


Second you think that number 1 can be represented as 0.99999........ (
decimal) , well I think that this is only an approximate representation
that is not correct.
The only representation of 1 is 1.0000......... and to me
0.9999........... < 1.

If 0.9999........... < 1 then x = 1 - 0.9999... > 0

So how much larger than zero is this x?

Is it large enough so that x/2 is smaller?

[x/n] + [x/(n^2)] + [x/(n^3)] +.............+ [ x/(n^k)] = [x/(n-1)] -
[ x/{ ( n^k) ( n-1 ) } ]

For n=2,3,4,5,.............
and K= 1,2,3,4,5,............

now 0.99999............ = 9/ 10 + 9 / 10^2 + 9 / 10^3 +
....................= 9/9 - 9/[ (10^Omega) *9} = 1 - [1/(10^Omega)]

10^omega is not a number; it is an ordinal, but it is not a
number. (10^omega)*9 is an ordinal, but not a number.

No you are wrong. Omega is a Transfinite Ordinal number. review
Cantor.

Which is what I said. In this context, "number" refers to "real
number". Duh.

Also number 9 is an ordinal number.

Can you tell me what is the difference between real number and ordinal
number.

Can you?

An ordinal is a well-ordered set such that for each a in A,
a = {x in A : x<a}.

A real number is many things, depending on your construction: it can
be a Dedkind cut of rationals, or an equivalence class of Cauchy
sequences of rationals, etc. In any case, it is not "a well-ordered
set such that for each a in A, a = {x in A : x < a}.

Division of ordinals is undefined. So 9/[ (10^omega)*9] is nonsense.

Subtraction of ordinals is undefined; so even if 9/[(10^omega)*9] were
some meaningful ordinal, "9/9 - 9/[ (10^omega)*9]" would be nonsense.

Even if 9/9 - 9/[ (10^omega)*9] made sense as an ordinal, the left
hand side of your "equation" is a real number, and the right hand side
is an ordinal. So the expression you have would STILL be nonsense.

Your reply is nonsensical. All numbers 9 and 10 and Omega can be
ordinal numbers.

And how, pray tell, Oh Great And Glorious One, do you define quotients
and subtraction of ordinals, which is exactly what I said above?

Duh.

I notice, by the by, that all your nonsensical gyrations failed to
answer his question.

Wrong.

No. The post failed to contain an answer to the question. Its entire
contents were nonsense. And you are quite clearly either a crank or a
troll. Bye.

--
Neither, just one who wants to learn!

I confess I have scarce mathematical knowledge, and I don't insist on
my beleives, I am only questioning to know the truth.

From what I know from Bertrand Russell's books Number x is the class
of all similar classes containing x members ( the definition seems
cyclic but it is not ). similar classes means the existence of one to
one relation between their members ( bijection).

So number two is the class of all doubles and number three is the class
of all triples. Review " Introduction to mathematical philosophy".

An Ordinal number is the number terms in a series, it is not the
series. It is the class of all similar series.( similar has the same
meaning above).

A cardinal number is the number of members in a set, ie the class of
all similar sets, and it is not affected by order.

What is a real number ? I don't have an exact definition , but from
what is writtin in this forum it seems to be a number which possess
inductive properties, the kind of a number Bertrand Russells refers to
as inductive number or finite number, perhaps?.

I heard that division is not defined for ordinals , but I don't know
why? Division of transfinite cardinals by finites is defined, why for
transfinite ordinal numbers is not defined I don't really know.

However addition multiplication and even exponentiation is defined for
ordinals.

you say that 1/ (2^ Omega ) is non sense, perhaps but I don't know why
it is so. why division and subtraction is not defined for ordinals?






======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

Relevant Pages

  • Re: Question
    ... Arturo Magidin wrote: ... zuhair wrote: ... Omega is a Transfinite Ordinal number. ... and subtraction of ordinals, which is exactly what I said above? ...
    (sci.math)
  • Re: well-ordered sets and inductive sets
    ... >Consider the transitive set construction of the ordinals. ... if he had that very precise definition of "succesor" ... Arturo Magidin ...
    (sci.logic)
  • Re: Question
    ... zuhair wrote: ... Arturo Magidin wrote: ... So the expression you have would STILL be nonsense. ... and subtraction of ordinals, which is exactly what I said above? ...
    (sci.math)
  • Re: well-ordered sets and inductive sets
    ... >>Arturo Magidin wrote: ... >>Consider the transitive set construction of the ordinals. ... the successor of each ordinal X is given by X U: ...
    (sci.logic)
  • Re: Small Set theory:Revised.
    ... P((y is a subset of Power y and every member m of y is a subset ... since otherwise it will be in itself and thus violates axiom 2. ... and accordingly all ordinals would be finite, and N would be the set of ... In zuhair set theory, the Axiom Of Choice is probably not needed. ...
    (sci.math)
Loading