# In mathematics is null == zero?

Kindly consider it soft question as I am a software engineer.and I know only software but I have a doubt in my mind that there would be something like null in mathmatics as well.

If Mathematics NULL IS Equivalent to ZERO?

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Could you specify? I would say no, because NULL is undefined, while ZERO = 0 is the number 0. –  Stefan Nov 16 '12 at 11:43
What is "NULL" in mathematics? You can define it to be whatever you want it to be. –  wj32 Nov 16 '12 at 11:46
@Stefan, I just meant to ask how mathematicians use the concept of NULL, not how that word might be arbitrarily defined; –  Manish Shrivastava Nov 16 '12 at 12:19
@ManishShrivastava: Then you need to describe the concept you're asking about to the mathematicians who answer, not just name it. For what it's worth, as a computer scientist, I don't even think the word "NULL" without further qualification describes any software engineering concept uniquely. Its meaning in C is subtly different from that in SQL, for example -- and yet different in JavaScript where "null" and "undefined" are explicitly not the same value. So you can't just ask how mathematicians use the concept without specifying which of the many "null" concepts you mean. –  Henning Makholm Nov 16 '12 at 12:25
Wikipedia's answer is interesting too. –  Raymond Manzoni Nov 16 '12 at 12:50

The distinction between the empty set $\emptyset$ and the number $0$ is similar to that between NULL and ZERO. For example, the set of real solutions (or informally "the solution") to $x^2=-1$ is $\emptyset$, but the solution to $x^2=0$ is $0$.

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Well, the set of real solutions to x^2 = 0 is {0}.. –  flindeberg Nov 16 '12 at 11:52
@flindeberg, yes, and by the same abuse of language we can say $\{0\} = 0$. Still, $\{0\} \ne \emptyset$. It is sort of like how in perl "0" is false even though it is a non-empty string, and also 0 == undef but defined(0) and !defined(undef). –  Dan Brumleve Nov 16 '12 at 12:04
My intention was to point out that the solution is the set (or enumeration) containing only 0, not 0 itself. Once we start simplifying by assuming that {0}==0 we are on very dangerous grounds (and by the way, assuming that NULL == 0) :) –  flindeberg Nov 16 '12 at 12:26
@flindeberg, yeah let's leave that rabbit hole alone. You are right about the value of precision in notation... When we are comparing apples and apples (sets and sets) then we are being absolutely precise and there is no need to quibble about meanings. I guess my point is just that it can be useful to discuss mathematical objects using a similar language, although it is often ambiguous. –  Dan Brumleve Nov 16 '12 at 12:32
Your answers is also considerably correct. But what I was looking into is I found it in Wikipedia. Thanks a lot. –  Manish Shrivastava Nov 16 '12 at 13:10

In my mind there is no need for a concept like NULL in mathematics if you think of NULL as in NULL-pointers.

NULL in this sense is a technical necessity because you cannot un-define a variable: Once a variable has been assigned a value, a certain bit of memory is reserved for this variable and this memory is marked as re-usable only if the variable goes out of scope (simplified speaking).

You cannot say "The variable with this name doesn't exist anymore." without letting it go out of scope, because that would make language interpretation much more complicated without many benefits. Therefore, to indicate that the value of the variable has no meaning, one uses NULL.

What NULL stands for in the end depends upon the programming language: In some it is a special keyword, but in some it is also just a different name for the integer $0$.

You can assign an arbitrary value to NULL in mathematics as mentioned in the other replies ($\emptyset$, $0$, etc.) but as mathematics has nothing to do with memory allocation there is really no need for such a thing as NULL.

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In 'mathematics' everything is possible, and in theory everything is renamable. So, we can have a theory where 'Zero' and 'Null' have different meanings, however you want to mean it..

For example, we can just consider the set of natural numbers $\Bbb N$ equipped with one more element, which we can call 'null', and we can denote it anyhow, e.g. '$O$'. And we can require whatever it should satisfy (until it is not bringing a logical contradiction to something), for example:

Let $O+x:=x$ for all $x\in\Bbb N$, and let $O\cdot x:= O$ for all $x\in\Bbb N$. (In particular, $O+0=0$, $O+1=1$, $O\cdot 0=O$.) So that we will have a zero $0$ and a 'null' $O$, if you like, in this structure $(\Bbb N\cup\{O\},+,\cdot)$.

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I think the question is about how mathematicians use the concept of NULL, not how that word might be arbitrarily defined; although it is not a standard terminology, I am not reading this as a "terminology" question either. NULL has different specific meanings in different programming languages, but what is being asked is how are those meanings unified in mathematics. –  Dan Brumleve Nov 16 '12 at 11:56
Yes, but the given same words may have different interpretations in the various fields (theories) within mathematics. And I argue, that you can build any kind of theory, following the specific interpretations that you have in mind for those words.. –  Berci Nov 16 '12 at 11:59
Indeed, and that POV is a good contribution. Upvoted! –  Dan Brumleve Nov 16 '12 at 12:00
Your answers is also considerably correct. But what I was looking into is I found it in Wikipedia. Thanks a lot. –  Manish Shrivastava Nov 16 '12 at 13:09

Thats what I wanted to get

# Ref : Wikipedia

In mathematics, the word null (from German null, which is from Latin nullus, both meaning "zero", or "none")[1] means of or related to having zero members in a set or a value of zero. Sometimes the symbol ∅ is used to distinguish "null" from 0.

In a normed vector space the null vector is the zero vector; in a seminormed vector space such as Minkowski space, null vectors are, in general, non-zero. In set theory, the null set is the set with zero elements; and in measure theory, a null set is a set with zero measure.

A null space of a mapping is the part of the domain that is mapped into the null element of the image (the inverse image of the null element).

In statistics, a null hypothesis is a proposition presumed true unless statistical evidence indicates otherwise.

Other answers are also considerably correct. But what I was looking into is I found it in Wikipedia. Thanks a lot.

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As an instance, in measure theory, empty set $\emptyset$ as well as the set of rational numbers $\mathbb{Q}$ has measure zero. $\mathbb{Q}$ is certainly not an empty set however, from a measure theoretic point of view, these are both null sets. –  Deniz Nov 16 '12 at 13:36