Maurile Tremblay said:
Ilov80s said:
Is zero a number or the absence of a number?
It's a number.
I agree, but similar to some of the earlier discussion, zero is a number kinda because we've defined it as such. (This goes a little beyond my pay grade, but IIRC we can and do study algebraic structures like semigroups that don't contain an additive identity.) The same way we define negative numbers as additive inverses, or 1/2 as a number, or
i as a number, or really anything else in math. Even the existence of something as seemingly obvious as the number 2 is ultimately founded on some set of axioms that we just sort of accept as true, and upon which we build definitions of everything else.
I remember getting into an argument with my brother about the score of a football game that had just started. He said it didn't have a score. I said it did have a score: the score was zero to zero. That's a score.
The score of the game is "zero to zero," which isn't a number, it's a string representing the state of the game.
When the game has first started, you could ask, "How many points have the Giants scored?" and I might respond, "They
haven't." In that sense, one might argue that 0 isn't the number of points scored, it's merely the way we describe an absence of points.
Anyway, like I said, I don't disagree with you, just providing a different take. To the side that might argue that numbers must correspond to physical representations, can you give me pi apples (not to be confused with apple pie, of course)? Is pi not a number?
Numbers, like other mathematical constructs (such as the order of operations), are for the most part what we agree they are. Whether zero is or isn't
really a number is a pointless but possibly fun philosophical diversion.