Maximal meaning

măksə-məl
(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).
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Of, relating to, or consisting of a maximum.
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Being the greatest or highest possible.
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An element in an ordered set that is followed by no other.
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Highest or greatest possible; of or constituting a maximum.
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Largest, greatest (in magnitude), highest, most.
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(mathematics) The element of a set with the greatest magnitude.
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(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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Origin of maximal