Definitions
1.AdjectiveLargest, greatest (in magnitude), highest, most.
2.AdjectiveLarger than any previous term in the sequence."In the sequence (1, 2, 10, 5, 12, 6), the fifth term, f(5) = 12, is a maximal term, as each of the first 4 terms are smaller than 12."
3.AdjectiveSuch that no other element is greater (with respect to the given partial order)."With respect to the ordering induced by set-theoretic inclusion, the set
{
{
2
}
,
{
1
,
2
}
,
{
2
,
3
}
}
{\displaystyle \{\{2\},\{1,2\},\{2,3\}\}}
has two maximal elements:
{
1
,
2
}
{\displaystyle \{1,2\}}
and
{
2
,
3
}
{\displaystyle \{2,3\}}
"
4.NounThe element of a set with the greatest magnitude.
5.NounSaid 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).
6.NounSaid 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.