On Oct 9, 11:10 pm, Frederick Williams <freddywilli...@btinternet.com> wrote: > Alen wrote: > > > From the discussions on this thread I think > > that perhaps I have not succeeded in conveying > > what I meant by space as an infinity. So I shall > > try to make it clearer by an analogy. > [...] > > > I have not tried to apply this kind of notion of > > an 'infinity as object' to mathematical infinities. > > If you are concerned with the infinities of physics, then disregard my > contribution to this thread. But you did post to sci.math after all...
I am interested in infinity as applied to maths in a basic sense, I suppose I might say, but I am not familiar with, and have not studied, the kind of extended debate about sets and such like that you indicate below
I posted to sci.math in case mathematicians might see someting of interest in a discussion of the concept of infinity :)
> > For example, is there some kind of 'object' such > > that the integers exist as its 'property'? I don't > > know. It would be necessary to try to identify > > what kind of an object it might be. > > Properties are sometimes thought of as subsets of some "universal" set. > (Don't take the word "universal" too seriously, it means something like > "set inclusive enough to contain everything currently under > discussion".) Integers can be construed as sets and therefore subsets > of some other set. A very simple example can be got by considering > natural numbers rather than integers. According to one definition of > natural number they are subsets of a set called omega. Also, according > to that definition, one might say that three (for example) is the > property "being less than three". That probably looks circular hut if > you start with nought = the property "being less than nought" = the > empty set (remember, we are considering the natural numbers only) and > work your way up, it isn't. Look up "von Neumann ordinals". For > integers, it is messy. > > -- > When a true genius appears in the world, you may know him by > this sign, that the dunces are all in confederacy against him. > Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting