The Numerical Super Bowl

How about a great sports event? It is more universal than any championship game. It is zero against infinity.

Whenever we multiply zero by any number zero always predominates.

Zero x 5 = zero

Zero x 13 = zero

Zero x 27 = zero

Whenever we multiply infinity by any number infinity always predominates.

Infinity x 5 = infinity

Infinity x 13 = infinity

Infinity x 27 = infinity

So here is the question. What happens if we multiply zero by infinity? Does zero predominate or does infinity predominate?

Does zero x infinity = zero or does zero x infinity = infinity?

I have a feeling that the majority of people would choose zero. We are taught since early childhood that zero multiplied by anything equals zero. But I find that infinity actually has a few things going for it.

First is that while both predominate over finite numbers in multiplication, only infinity predominates in addition and subtraction. 5 + zero = 5 but 5 + infinity = infinity.

Second is the question of our inherent bias. The majority of people would probably choose zero. But are we really qualified to make an unbiased choice? We are much more familiar with zero than we are with infinity. We see zero all day in measurements and on digital clocks. We are only too familiar with zero in that it is what we have if we start with a certain amount of money and then spend that amount. In contrast infinity is a hazy and nebulous concept that has no practical meaning to most people. This familiarity gives us an unfair bias to choose zero over infinity.

Third is that, while zero multiplied by any number equals zero, infinity is such a vast number that ordinary rules do not apply. Parallel lines are defined as lines in the same geometric plane but which never meet. At least the lines never meet in the finite universe, but are defined as meeting at infinity.

Based on all of this I am going to go with infinity. Infinity is so infinitely vast that ordinary rules do not apply and even zero x infinity = infinity.