Post Closed as "unclear what you're asking" by Anton Trunov, vonbrand, David Richerby, Juho, Evil
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DFA: Why is the transition function not a set?

The DFA is a 5-tuple ($Q,\sum, \delta, q_0, F$) where

-finite set of states ($Q$)
-finite set of symbols called the alphabet ($\sum$)
-a transition function ($\delta: Q \times \sum \rightarrow Q$)
-an initial or start state ($q_0 \in Q$)
-a set of accept states ($F \subset Q$)

Since in practice (programmatic implementation) the transition "production" (that is, $\delta(q_{from}, input) = q_{to}$) cannot be the same for all in $Q\times \sum$ and $Q$, then why is it not defined as "a set of transitions".