In mathematics, $\Bbb R$ is used to denote the set of all real numbers, and $\Bbb C$ is used to denote the set of all complex numbers. Is there a symbol used to denote the set of all constant numbers, meaning both real and imaginary?
For example, $c \in \Bbb R$ can be used to state that $c$ exists within the set of real numbers, and $c \in \Bbb C$ can be used to state that $c$ exists within the set of complex numbers.
Is there a symbol used in the same way, $c \in ?$ to state that $c$ is a constant and never changes? Otherwise, when can it be inferred that the variable in question (in this case $c$) is a constant?
Best Answer
$R,C$ are not really at all standard notations for a real or complex number. I've seen a wide variety of letters to represent real numbers (somewhat moreso $x$ or $y$, sometimes $a$), and often $z$ to represent complex numbers, but I don't believe there is at all a standard notation for these numbers. Names are rather arbitrary after all. I think you might be thinking of $\mathbb{R}$ or $\mathbb{C}$, which denotes the sets of real and complex numbers respectively (as opposed to any single one).
As for something to denote a constant? Use any letter of your choice. About the only letters I would suggest you don't choose are those associated with other common constants ($\pi, e, i, \gamma$, etc) - which isn't even really "illegal" as much as it can be confusing for a reader.
I guess if I had to say which I've seen more commonly denoting an arbitrary constant, it would be $c, C, k, a,$ and $A$. But again, it's arbitrary -- aside from well-known constants, it's pretty much completely arbitrary what to name an arbitrary constant; if there is a "standard" for any of these, I'm unaware of it. At best there is just a lot of people using the same variables for the same things for whatever reason, but there's no requirement on that.