Ah yes, the number 0. It’s kind of an odd thing to think about, since zero is essentially nothing, and our minds have a hard time understanding the concept of nothing. In fact, people have debated that maybe zero isn’t even a number at all- that it’s just a concept, similar to infinity. I for once was curious to see this kind of argument pop out, because as long as all of us can remember, we’ve been taught that 0 is in fact, a number, and saying otherwise just wouldn’t make sense to our brains that were hard-wired to think so. With that in mind, let’s take a deeper look into it.
Source: Life Through A Mathematician’s Eyes
In terms of philosophy, you can’t really have a zero of things, because anything that’s zero means it doesn’t exist. This makes sense in a manner, but it gets more complicated when you realize that if you count the number of things that don’t exist, you would get an infinite number of them- as there is no limit of things you can think of that don’t exist. This makes it seem like zero is just a mere concept that’s closely related to infinity.
Now once we go out to the mathematical side of things, you also realize that some equations and concepts go haywire when you deal with 0, the most notable being anything divided by 0 is undefined, and that anything multiplied by 0 is zero. Again, it’s just like infinity. Anything divided by infinity is, well, an infinity that approaches zero, and anything multiplied by infinity is infinity.
Furthermore, quite a lot of mathematical rules always have exceptions where it can’t be applied if a number is equal to 0.
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The list goes on. In a game, if you have 1 point and your opponent has 2, your opponent has twice as much points as you; whereas if you have 0 points and your opponent has 2, well, the whole thing falls apart. You also can’t have a circle with radius zero, and it’s neither positive nor negative.
However, despite all these arguments, all mathematicians will give you this answer: “zero is indeed a number.”
While infinity and zero have many similar properties, zero is much more consistent and far less troublesome than infinity. Anything added and multiplied by infinity is infinity, and anything subtracted or divided by infinity is an infinite decimal approaching 0. But with 0, you get very definitive answers. When you add or subtract anything to zero, the answer is the number itself. When you multiply by zero, the answer is 0. It almost just as definitive as any number, compared to infinity which is just weird and inconclusive.
Algebra also pretty much needs a zero, because you can’t have an additive inverse without the additive identity. Like when you solve for x+5=1, you add 5’s additive inverse to both sides, as anything added to its additive inverse is zero, hence x+5+(-5)=1+(-5) x=-4. You definitely can’t do that without a zero, as most of algebra revolves around it.
And yes, you can’t have 0 things, like zero apples, but you also can’t have negative apples; you also can’t have a circle with a negative radius. So arguing that 0 isn’t a number under those pretenses also means that you’re saying all negative numbers aren’t numbers either. Zero and negative numbers are simply extensions of the concept of counting, taking it beyond the normal.
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Basically, zero works in most settings, whilst infinity works in almost none of them. Zero mostly gives definitive answers, while infinity doesn’t. It’s definitely peculiar, yes, but that doesn’t mean it’s not a number; it’s just a different kind of number.
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