THE MYSTERIOUS ZERO/INFINITY
A new deck of 52 cards usually has two jokers. Likewise there are two jokers that bedevil physics -- zero and infinity. They represent powerful adversaries at either end of the realm of numbers that we use in modern science. Yet, zero and infinity are two sides of the same coin -- equal and opposite, yin and yang. "Multiply zero by anything and you get zero. Multiply infinity by anything and you get infinity. Dividing a number by zero yields infinity; dividing a number by infinity yields zero. Adding zero to a number leaves the number unchanged. Adding a number to infinity leaves infinity unchanged." Yet, the biggest questions in science, philosophy, and religion are about nothingness and eternity, the void and the infinite, zero and infinity.
IF 0 and infinity are indeed two sides of the same coin, as, for instance, Charles Seife posits in:
Zero: The Biography of a Dangerous Idea
...then how is it we seem to treat these two entities so differently?
If we can speak of 0 + 1, then why not infinity - 1?
For myself, in order not to run afoul of scientific dogmas worthy of 17th Century Italy, I have taken to referencing "infinity" by using the term "Z" to denote "virtual infinity," a number as big as the mind can imagine at any given point in time, a number so big, in fact, that it falls just this side shy of being a "concept."
And the flip side of Z?
Because 0 is not just "virtual nothing" but actual nothing. In other words, I would posit, the flip side of... infinity. Yet, while the one is considered a number, the other is considered a "concept." To my way of thinking, this creates a false "apples vs. oranges" thought scenario that hinders rational analysis.
P.S. THE STANDARD VIEW(S)
Is zero a number?
The simple answer: Yes, of course zero is a number. (I'm giving you the benefit of the doubt and not saying, "you dolt.") What, you think it's maybe an animal or vegetable?
The mathematical answer: Well, it depends on what you mean by "number." This is not sarcasm, there are different sets of numbers that build up to the Real Number system (the unique complete ordered field).
Zero is clearly an element of the set of Real Numbers, it's the "additive identity" -- the number that, when added to any other number x, doesn't change the value of x. (Similarly, 1 is the multiplicative identity -- the number that, when multiplied by any other number x, doesn't change the value of x.) Thus, zero is a number, just as any other element of the set of Real Numbers is a number.
What is infinity?
Infinity is not a number; it is the name for a concept. Most people have sort of an intuitive idea of what infinity is - it's a quantity that's bigger than any number. This is sort of correct, but it depends on the context in which you're using the concept of infinity (see below).
There are no numbers bigger than infinity, but that does not mean that infinity is the biggest number, because it's not a number at all. For the same reason, infinity is neither even nor odd.