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If <math>L_1<math> and <math>L_2<math> are formal languages, then the left quotient of <math>L_1<math> with <math>L_2<math> is the language consisting of strings w such that xw is in <math>L_1<math> for some string x in <math>L_2<math>. In symbols, we write:
<math>L_1 / L_2 = \{w \ | \ \ \exists x \in L_2 \ \ : \ \ xw \in L_1\}<math>
You can regard the left quotient as the set of postfixes that complete words from <math>L_2<math>, such that the resulting word is in <math>L_1<math>.
For more details, see right quotient.
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