ZF Axiom of Infinity: Natural Numbers Exist

  • Thread starter Thread starter CRGreathouse
  • Start date Start date
  • Tags Tags
    Axiom Infinity
CRGreathouse
Science Advisor
Homework Helper
Messages
2,832
Reaction score
0
In ZF, the axiom of infinity says that the set of natural numbers exists. I was wondering if there was a (finitist?) weakening of ZF that included the axiom "the class of natural numbers exists".
 
Physics news on Phys.org
Wait, this is a dumb question, isn't it. This actually follows from a suitable definition of classes and ZF - the axiom of infinity.

Sorry. :redface:
 

Thread 'Here's a Statistics problem for game of Polo (or Hockey if you like)'

Namaste & G'day Postulate: A strongly-knit team wins on average over a less knit one Fundamentals: - Two teams face off with 4 players each - A polo team consists of players that each have assigned to them a measure of their ability (called a "Handicap" - 10 is highest, -2 lowest) I attempted to measure close-knitness of a team in terms of standard deviation (SD) of handicaps of the players. Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that...
View full post »

Thread 'Roulette wheel physics and probability'

Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
View full post »

Similar threads

A Formal axiom systems and the finite/infinite sets
Replies
10
Views
2K
ZF Set Theory and Law of the Excluded Middle
Replies
1
Views
2K
How to construct the natural numbers with hypersets
Replies
5
Views
2K
Is the Empty Set Axiom a Theorem in ZF?
Replies
13
Views
6K
I ZFC .... Axioms of Foundation .... and Infinity ....
Replies
4
Views
2K
MHB ZFC .... Axioms of Foundation .... and Infinity ....
Replies
9
Views
3K
A An additional constraint to the ZFC axioms?
Replies
40
Views
4K
I Are existence proofs outlawed in multi-valued logics?
Replies
19
Views
3K
A About the “Axiom of Dependent Choice”
Replies
2
Views
2K
MHB About the “Axiom of Dependent Choice”
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top