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[Asmodean]

What is the result of multiplying infinity by zero?

A good example of it depending on your frame of reference.

Common elementary school scalar algebra would have you think that multiplication by zero will yield zero - and it does within that frame of reference. In the realm of vector spaces and rings, however, it may very well not with varying degrees of "real" or semantic differences.

EDIT: consider the following vector space examples: (0,0,1)x(1,0,0) = (0,1,0). (0, 1)x(2, 0) yields a scalar. So does (0, 0)x(2, 1) (The latter just yields a scalar zero, that is, having no directional component and ""no"" magnitude - the former has no directional component, but ""a"" magnitude*)

RE-EDIT at a later date: I may have brain farted a little and neglected the example of vector-scalar multiplication, which is probably the most telling. (1,2)*0 is not 0. It is (0,0) The difference is that while each component of the end vector may have been reduced to zero in magnitude by multiplication, the vector itself remains, in this case, two-dimensional. Thus, it's not "a dot on a line," but rather, "a dot on a plane."

So to answer your question, I would have to ask, "what is it you are trying to multiply with what, precisely?"

*Before mathematicians in the audience descend on me demanding righteous vengeance, for the purpose of this example, I am indeed equating "no" and "a" with "zero-" and "non-zero-" respectively.

[zorkan]

Sorry, I don't understand your maths.
Isn't zero a mathematical trick?
Does infinity exist?
Could you add or subtract to it.

[Asmodean]

Sorry, I don't understand your maths.

That's fine, and also a bit of why I did not try and expand upon rings - in my view, vectors are a little more intuitive.

If you would like, I can explain the math behind my examples.

Isn't zero a mathematical trick?

Not at all. It can be a magnitude or a quantity or a condition or a vector component, and useful as such. It can also be a way of expressing the number of apples in my coffee cup. It has some interesting properties here and there, but... No, I wouldn't say that there is any "trick" to it.

Does infinity exist?

As a concept? most certainly. As "tangible" physical reality? Not within a finite Universe. (The problem of running out of bits would catch up to it eventually. Given an infinite Universe, or an "without" it, however... Maybe.)
 

Could you add or subtract to it.

Of course. And multiply and divide by it. You can do all sorts of mathematical operations with infinities, to varying degrees of practical usefulness.