Maximal vs. Maximum

Difference Between Maximal and Maximum
Maximaladjective
Largest, greatest (in magnitude), highest, most.
Maximumnoun
The highest limit
Maximalnoun
(mathematics) The element of a set with the greatest magnitude.
Maximumnoun
(mathematics) The greatest value of a set or other mathematical structure, especially the global maximum or a local maximum of a function
Maximalnoun
(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).
Maximumnoun
(analysis) An upper bound of a set which is also an element of that set
Maximalnoun
(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.
Maximumnoun
(statistics) The largest value of a batch or sample or the upper bound of a probability distribution
Maximaladjective
the greatest or most complete or best possible;
maximal expansionmaximum pressureMaximumnoun
A 147 break; the highest possible break
Maximumnoun
A score of 180 with three darts
Maximumnoun
A scoring shot for 6 runs
Maximumadjective
To the highest degree.
Use the proper dose for the maximum effect.Maximumnoun
the largest possible quantity
Maximumnoun
the greatest possible degree;
he tried his utmostMaximumnoun
the point on a curve where the tangent changes from positive on the left to negative on the right
Maximumadjective
the greatest or most complete or best possible;
maximal expansionmaximum pressure