Quote:
Originally Posted by Merkin Muffley
Sorry, I didn't catch that.
That's my point 
I wouldn't say infinity is undefined. You just can't expect it to behave like the numbers do. It wasn't brought up properly.
I've certainly seen applications for such systems, but you have to recognize, if you allow this sort of operation, there is a price to pay.
I've seen various totally rigourous systems of mathematics that include conventions about what 0 times infinity is, or things like that. You just have to recognize that infinity can't be manipulated like a number, and make sure the additional rules you introduce to manipulate infinity are consistent with themselves and the existing rules. |
Zero times infinity is perfectly OK within the usual cardinal and ordinal number systems. It is zero. It doesn't matter which "infinity" you are talking about (and yes, in the cardinal and ordinal systems there are different sizes of infinity and it makes perfect sense). This is absolutely consistent with the Zermelo Fraenkel, plus choice, axioms for set theory. There is no problem whatever with this. You can see a simple explanatin of the cardinals and ordinals in Halmos's little book
Naive Set Theory.
It has NOTHING to do with 1/0, which is simply undefined and meaningless.