Is there any symbol for "undefined"?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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".

Answer 4

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.