Re: Weniger als alef

On 11 Nov 2005 02:12:03 -0800, "WM" <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

>
> Ach? Numbers sind nun nur noch die natürlichen?
>
Ja, in diesem Kontext schon. Ich zitiere mal vollständig:

---------------------------------------

Peano's Axioms:

1. Zero is a number.

2. If /a/ is a number, the successor of /a/ is a number.

3. Zero is not the successor of a number.

4. Two numbers of which the successors are equal are themselves equal.

5. (induction axiom.) If a set S of numbers contains zero and also the
successor of every number in S, then every number is in S.

Peano's axioms are the basis for the version of number theory known as
Peano arithmetic.

---------------------------------------

Source:
http://mathworld.wolfram.com/PeanosAxioms.html

Zweifellos wird hier unter einer /number/ eine natürliche Zahl
verstanden.


A.


--

E-mail:
amicus<at>simple<bindestrich>line<punkt>de
.

Relevant Pages

  • Re: Equivalency Function
    ... What, let's see here, so you are saying that infinity and zero are not ... without having the separate zero and infinity axioms (they're not ... the collection of ordinals, ...
    (sci.math)
  • Re: proving that a statement is undecidable
    ... it seems like you could never use Zermelo-Frankel axioms ... of GC in ZF but you can never find a counterexample either. ... There exists an element zero. ... Every element has a successor. ...
    (sci.math)
  • Re: Weniger als alef
    ... Zero is not the successor of a number. ... >> Peano's axioms are the basis for the version of number theory known as ... Andernfalls hätte man eben irgend eine Menge wie IR, die ...
    (de.sci.mathematik)
  • Re: Pa without 0 and successorfunction
    ... zero and the successor functions as primitive symbols. ... and S are not primitive symbol anymore so they should not be used as ... What you do is you add axioms which assert that there is a unique ...
    (sci.logic)
  • Re: infinity
    ... >>>system of axioms, the axioms are absolute. ... But, if you divide both sides by zero, you can get ... >> induction to prove an inequality which is decreasing with each iteration. ... > to establish its initial case, not the fact that the infinite sum ...
    (sci.math)