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What does maximal mean?

Looking for the meaning or definition of the word maximal? Here's what it means.

Adjective
Noun
  1. (mathematics) The element of a set with the greatest magnitude.
  2. (mathematics) Said of an ideal of a ring or a filter of a lattice: that it is as large as it can be without being trivial (improper).
  3. (logic) Said of a set of well-formed formulas: that it is as large as it can be without being inconsistent; i.e. that for any well-formed formula φ, the set contains either φ or ~φ.
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