In mathematics is null == zero?

Question

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?

Answer 1

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 $0$.

Answer 2

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 $(\Bbb N\cup\{O\},+,\cdot)$.

Answer 3

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.

Answer 4

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.