# Is zero a number or the absence of a number?

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I have looked at several different articles/explanations but they either have contradictory statements or they use esoteric language that I cant wrap my head around. pls help

In: Mathematics Yes it’s a number. -1 is a number as well. Pi is also a number. I’m not sure how anyone would argue that it isn’t a number. It is just the absence of whatever someone may be counting. Zero is definitely a number.

When you’re measuring or counting something, zero represents the absence of that thing – but that doesn’t mean that zero itself isn’t a number, it’s actually a very important number!

Almost all of the math we learn in school and use in everyday life and also in banking, science, engineering, and elsewhere all depends on there being a number zero to work with. 0 is a numeral. It denotes in the number it is part of that there is nothing in its place.

For example. The number 40. 4 in that is a numeral denoting that there are four lots of tens and 0 in that is a numeral denoting that there are zero lots of ones.

So, in the number 0 the numeral 0 denotes that there are zero lots of ones. A number can be defined as a quantity or amount. If I have none of something, then the quantity (or number) that I have of it is zero. Yes, zero is a number.

First, you have to consider the definition of “number.” In the mathematical sense, numbers are “objects” (fancy way of saying they’re things, just like a fish is a noun-thing and a cloud is a noun-thing). Number-things are just abstract is all, like the concept of “love” is a abstract thing. And number-things represent amounts, quantity, size, etc.

So if you have three dots (. . .) or three m’s (m m m), the “threeness” is the same between them. Three is a thing independent of the m’s and dots.

Zero fits into this idea just fine. It’s the absence of dots ( ) and the absence of m’s ( ). The “zeroness” is the same regardless of what we are talking about. It is still a number. Maybe a special number, but so is pi (it is irrational, not a counting number, etc). From a programmer perspective zero is a number: for example if you have 1+0 the result will still be a number.
But if you have 1+NaN(not a number) the results will be NaN.

From a mathematical point of view 0 is also a number, because it respect all the requirements to be one.
You know exactly where to find 0, you can use 0 in operations and 0 is a valid result.

But let’s think that 0 is not a number for a second.
If you have the equation x=1-1
I would say that x=0 but if 0 is just the absence of a number, I should probably say that x does not have a value [removed] It kind of depends.

As far as a computer is concerned it’s typically two different things. 0 can be a number, or there can be nothing.

The most obvious example is in excel. You can have an empty cell. Make a formula referencing that cell trying to add it and it wl treat it as 0, make one looking for text and it will treat it as “” (blank). But that’s only because excel knows this nuance, try and get more complicated formulas that reference different formulas and it will very quickly through an error at you because it doesn’t know what it’s looking at.

Outside of programming/computers I can’t think of an example where it would matter outside of a philosophical debate

There is a small arguement that saying 0 in a scientific sense implies some kind of accuracy: generally it would be 0.0 implying that there can’t be more than 0.04. but if you say “nothing” that means absolute 0.

That’s a very niche scenario though. 0 is as much of a number as any other number. Whether numbers exist or not is a philosophical question. Depending on how you view numbers, one might say that some numbers exist but that 0 doesn’t. But it doesn’t really matter if it exists or not, it’s still a number, and a very useful one at that. Zero is a number. it has certain properties that may look trivial, but it is important that a number exists which has trivial properties.

There are mathematical structures that don’t have a zero, or have other properties you would not expect from zero. These are still important, but usually not associated with numbers. zero is a number representing a value of nothing. It in itself is not the absence of a number. If numbers are a roll of toilet paper zero is a roll with no paper on it. The roll is still there, you can clearly see that it is a roll hanging from the wall, but there is no paper on the roll. That is zero: A number who is there to indicate no value. Modern mathematics is formalized in the so called “peano axioms”.
This is a set of statements that define what is a number and how numbers behave.

The first peano axiom is exactly your answer: “**0 is a natural number**”.

https://en.wikipedia.org/wiki/Peano_axioms I do believe Zero is a number. All numbers are just concepts. 1 baseball is a baseball, two base balls are just 2 individual balls but the concept of 2 is the grouping of them. The label we put on the size of the group. The label we put on no baseballs is zero.

Side note:
I do not however believe in negative numbers. Not that the concept of them doesn’t exist but a -4 and a 4 are really the same.
You buy an object, its cost is 10 dollars, you have 6. You borrow 4 dollars from a friend. You now owe him 4 dollars. You could say you have -4 dollars. But negative dollars don’t exist, it’s still 4 dollars. No negative apples, wrenches, dollars, or baseball cards. Just a postive version of the object. Zero is a called an identity under addition. Under multiplication the identity is 1. Try and see the similarities and also see how it is associated with an operator: 0 with addition, 1 with multiplication.

So get any number *x*: x + 0 = x; x.1 = x. So under addition, 0 leaves your number alone; under multiplication, 1 leaves your number alone.

What’s important is to remember numbers come packaged with operators that do things to numbers. 0 has some special properties but they’re not something weird because 1 also has those properties just under a different operator. Numbers are just labels that behave a certain way with respect to operators.

That’s why you learn multiplication tables and addition tables. It’s the relationship not the labels that are important.

Now back to your question. These numbers also represent the size of a collection of things. If we have a cow, and another cow, and another one: we say there are 3 cows. What’s amazing is these labels that represent the size of collections also follow the rules of numbers. If I have 3 cows and someone gave me 2 more cows I can look at my addition tables and find 2+3 gives me 5 which amazingly is the number of cows I now have. If I gave all my cows away I now have no cows. This is 5 – 5 = 0 cows.

So 0 represents a few things. The difference between having two collections of the same number of things. The size of an empty set. The addition identity in a number system.

It wears a lot of hats – like numbers usually do. This can get it confusing if you want to go philosophical about it. There are different “sets” of numbers: real numbers, integers, rational numbers, irrational numbers, imaginary numbers, etc. These are mostly mathematical terms that categorize numbers depending on how they behave in mathematics. In these categories, zero is an integer, a real number and a rational number.

In other words, it behaves mathematically like a “number.”