Post Closed as "unclear what you're asking" by Anton Trunov, vonbrand, David Richerby, Juho, Evil
2 edited tags
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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".