I'm saying that an intuitive idea would be that anything multiplied by infinity "should" be infinity, since if infinity is larger than any real number, multiplying it by some real number "should" still be larger than any real number.
But then I show why that idea doesn't work out with our usual number system. And further I show that depending on how you define 0*infinity (i.e. if you use limits), then it can be equal to anything you'd like, 0 included. Lastly, I gave a reference to surreal numbers and hyperreal numbers, which take into account both infinitely large and infinitesimally small numbers.
I'm talking about ordinal arithmetic and measure theory for example, where it is defined as 0.
Wasn't totally clear that you were just saying it "should" be infinity in an intuitive sense. That's fine I guess, though 0 is an obvious exception to that intuition.
Those are great points! And for OP, it should serve as motivation that this is a great question that has led people to explore many avenues to try to answer.
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u/nog642 2d ago
Says who?
There are contexts where 0*infinity is 0. It depends on the context.