Does 0 = Infinity?

[TheRealJoeFish]

They are both abstract concepts we use in our attempts to model and understand reality. They perform very different roles.

They are related by

1/n tends to infinity as n tends to zero

I came on to say essentially this.

To elaborate: although infinity and zero are not equal, the way you're thinking about them and the relation between them is certainly valid in some ways. What you're essentially getting at, I think, is that as 1 is to 1, and 1/2 is to 2, and 1/10 is to 10, 0 is to infinity (that is, infinity represents the multiplicative inverse of zero or vice versa). Although that doesn't exactly work in basic algebra, that thought does have applications in, say, complex analysis and topology. For instance, the Riemann sphere:



This thingy sort of wraps all of the complex numbers onto a sphere (by taking any number on the complex plane, drawing a line between it and the very top point of the sphere, and calling the intersection of that line and the sphere the "projection" of that number). It becomes complete only when you define that top point to be infinity, and, indeed, it does allow you to describe infinity as the multiplicative inverse of zero.

So, yes, they are certainly intricately related as Rob said. Not equal. But... One is the yin to the other's yang. Or something.