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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?

user574921
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  • No since "number" without any other context is ambiguous. As an aside, $\Bbb R$ is used to denote the set of real numbers and $\Bbb C$ is used to denote the set of complex numbers, not an individual real number or complex number. – JMoravitz Dec 14 '18 at 04:51
  • How would you use such a symbol? Depending on what you mean to say, there might be a standard notation, but we can't guess it without context. – Chris Culter Dec 14 '18 at 04:56
  • Thank you for the responses. I have edited my question to be more descriptive of the question I am asking. I also had previously forgotten how to enter math and I have added correct math into my question – user574921 Dec 14 '18 at 05:06
  • What do you mean by "any constant number" other than any complex number? Are you talking about $p$-adic numbers? Hyperreal numbers? – Robert Israel Dec 14 '18 at 05:14
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    I suspect that you are combining two different aspects of using variables. On one hand we may have information about what "kind" of number (or value) a variable is supposed to represent, as in your examples of real or complex numbers. On the other hand the role of a symbol plays as "constant" or "varying" could be combined with the other information, but is not exclusive of any particular domain of numbers. An author will need to explain to their Readers when and how a value of a symbol is fixed or (alternatively) is allowed to vary. – hardmath Dec 14 '18 at 05:18
  • Thank you all for the information. @hardmath is there a standard way to communicate that a value is fixed? – user574921 Dec 14 '18 at 05:28
  • It is an important point to make in writing up proofs to indicate when a value of one symbol depends on the value of another symbol. This is primarily done by careful exposition of the order in which values are chosen, but it is connected with the order of quantification in formal logic. An example is the definition of continuous function in terms of $\varepsilon$ and $\delta$. That is, the choice of $\delta$ will generally need to depend on the choice of $\varepsilon \gt 0$. Please edit your Question to give a firmer idea of what use you have for "constant" values. – hardmath Dec 14 '18 at 05:48

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$R,C$ 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.

PrincessEev
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