Notation for set of constant functions
I have a constant function that always returns the same integer value. How do I represent a set of functions where each function is a constant function that returns some arbitrary constant? For example, I would like to identify an element $f_p$ of this set as a function that always returns the integer value $p$. Similarly, $f_3$ would be a constant function that always returns $3$.
I'm also confused as to how I would define any arbitrary instance of a constant function. For example, if I had a function that always returned $2$, would I define it as $f: \mathbb{Z} \rightarrow \{2\}$?
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$\begingroup$Since your domain seems to be fixed throughout your argument, there is no need to make it visible to your reader. In these cases, it's quite common to write $c_x$ for the constant function $c_x \colon D \to \{x\}$, where $D$ is the fixed domain. Then $$ \mathcal C = \{ c_x \mid x \in X \} $$ is the collection of all constant functions with value in $X$ - for some given $X$. In your particular case, $$ \mathcal C = \{ c_z \mid z \in \mathbb Z\} $$ is the collection of all constant functions with integer values.
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