Difference between revisions of "Talk:Zermelo-Fraenkel Axioms"
(New page: I believe the axiom of infinity is incorrect; shouldn't it be that for all <math>a \in A</math>, <math>a \cup \{a\} \in A</math> as well?) |
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I believe the axiom of infinity is incorrect; shouldn't it be that for all <math>a \in A</math>, <math>a \cup \{a\} \in A</math> as well? | I believe the axiom of infinity is incorrect; shouldn't it be that for all <math>a \in A</math>, <math>a \cup \{a\} \in A</math> as well? | ||
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| + | Actually, the two forms are equivalent. There are in fact infinitely many possible different axioms of infinity, all of which are equivalent. The weakest and least specific of these infinitely many forms of the axiom is this: | ||
| + | * There exists a set <math>A</math> and a non-surjective injection <math>s: A \to A</math>. | ||
| + | I intend to write an article about this in a few days. Also, please sign your name when you write on talk pages using four tildes (<nowiki>~~~~</nowiki>). —[[User:Boy Soprano II|Boy Soprano II]] 15:12, 16 December 2007 (EST) | ||
Revision as of 15:12, 16 December 2007
I believe the axiom of infinity is incorrect; shouldn't it be that for all 
, 
as well?
Actually, the two forms are equivalent. There are in fact infinitely many possible different axioms of infinity, all of which are equivalent. The weakest and least specific of these infinitely many forms of the axiom is this:
- There exists a set
and a non-surjective injection 
.
and a non-surjective injection 
.I intend to write an article about this in a few days. Also, please sign your name when you write on talk pages using four tildes (~~~~). —Boy Soprano II 15:12, 16 December 2007 (EST)
