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For example we have $\frac{0}{0}$ which is undefined or we have a multiplication of $2\times2$ and $3\times3$ matrices which is also undefined. Is there any symbol for representing it?

user211859
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  • It is common to write "DNE" for "does not exist". – Ben Grossmann Jan 30 '15 at 22:58
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    My preferred symbol is not to write undefined things, the empty symbol. – Git Gud Jan 30 '15 at 23:00
  • @Omnomnomnom What about $\nexists$? – user211859 Jan 30 '15 at 23:00
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    I don't see that at all, and in this context it strikes me as "grammatically" incorrect. – Ben Grossmann Jan 30 '15 at 23:02
  • @user211859: That requires a subject, so it doesn't really represent anything. – Henrik supports the community Jan 30 '15 at 23:06
  • one way to show that under certain condition the value of interest does not belong to the set you're operating on. I.e. let's say y=f(x) is a function on a set of real numbers and f(x) becomes undefined if x=t, then you can say that iff x=t then y∉R. It might be convenient for scenarios when such undefined value actually belongs to the wider set (e.g. set of complex numbers if f is a square root and x is negative). – Alex Aug 01 '18 at 02:15

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According to a Wikipedia article on the subject, in Herbert B. Enderton's book Computability: An Introduction to Recursion Theory (2011), even if nowhere else (no other reference is given, and I've never seen the usage):

If $f$ is a partial function on $S$ and $a$ is an element of $S$, then this is written as $f(a)\!\downarrow$ and is read as "$f(a)$ is defined."

If $a$ is not in the domain of $f$, then this is written as $f(a)\!\uparrow$ and is read as "$f(a)$ is undefined".

Calum Gilhooley
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I have never seen such a symbol. I don't think it would be very useful, and it might make unexperienced people less aware that they are dealing with an undefined entity, and start doing calculations with it getting meaningless results.

Henrik supports the community
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  • Nothing >>= \a -> pure (a + 2) resolves to Nothing. Still better than undefined behavior, but at least you can chain computations, and if at any point your computation becomes undefined, all following computations are just ignored and Undefined is pipelined to the end indicating that your computation failed. That said, on paper it's a lot less useful, you know you made a mistake but you have no means of backtracing it. – Dmytro Dec 16 '16 at 08:31
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Usually one states "we leave the statement undefined". For instance, suppose we have the definition of convergence of sequence. Then

If a sequence $(a_n)_{n=m}^\infty$ is not converging to any real number, we say that the sequence $(a_n)_{n=m}^\infty$ is divergent and we leave $\lim_{n\to\infty}a_n$ undefined.

By other hand, in Computer science there are some symbols: undefined, null and NaN (not a number). But I've never seen something similar in math.

Cristhian Gz
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Because in mathematics undefined itself is defined, even elusive things like infinity or singularity.

$0/0$ is meaningless, instead of being undefined, and rational people don't do it. In programming it is a human error as well, and shall never happen if the code is bug-free.

Taozi
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