Traditionally, our notation has separated out a set and values associated with said set. We'll say something like the state is a tuple of $(V, f)$, where $V$ is a set of control values and $f$ is a vector of their corresponding costs. We then write their union as $(V \cup V', max(f_i, f_i')~\forall i)$. Instead, I want to write it like this: $V$ is a dictionary of control values to cost. It's union is $$ V \bigcup_{max} V' $$ Is that so bad? Or is there some other standard way of doing this that I should be aware of?

  • $\begingroup$ First off, I'm not sure "dictionary" means what you intend to people like me who do not use Python. (I see "dictionary" and think "Merriam-Webster".) Second, your union notation would not mean anything to me. I'm not sure there is a standard way of denoting what you intend. $\endgroup$
    – prubin
    Mar 1 at 18:40
  • $\begingroup$ What terms do you use besides dictionary? One-to-one table? Lookup table? Key-value set? $\endgroup$
    – Brannon
    Mar 1 at 18:56
  • $\begingroup$ In the context of mathematics (as opposed to coding) I would probably refer to it as either a function or a relation (either one-to-one or many-to-one as appropriate -- I believe the Python definition of "dictionary" rules out one-to-many). $\endgroup$
    – prubin
    Mar 1 at 20:05


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