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Topic: fom - 01 - preface
Replies: 4   Last Post: Dec 12, 2012 11:08 PM

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Posts: 18,076
Registered: 1/29/05
Re: fom - 01 - preface
Posted: Dec 12, 2012 2:01 PM
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On 12 Dez., 18:51, Alan Smaill <> wrote:

> A bad translation; it's not the domain that is real, but the numbers:

You agree that the numbers are real? But you do not agree that these
numbers are real numbers? Remarkable.

>    "The first number-class (I) is the set of finite integers
>     1,2,3, ...,nu,...,

And you have already forgotten that finite integers are real numbers?

> 3.14159...  does not make an appearance anywhere in these number classes.

Read § 4, first sentence:
Die erweiterte ganze Zahlenreihe kann, wenn es die Zwecke fordern,
ohne weiteres zu einer kontinuierlichen Zahlenmenge vervollständigt
werden, indem man zu jeder ganzen Zahl alle alle reellen Zahlen x, die
größer als Null und kleiner als Eins sind, hinzufügt.

Obviously these extended numbers are not ordinals or cardinals -
unless sets can have fractions of elements.

Regards, WM

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