Supremum vs. Maximum — What's the Difference?

(set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.

As great, high, or intense as possible or permitted

The greatest amount, extent, or intensity possible, permitted, or recorded

At the most

The greatest possible quantity or degree.

The greatest quantity or degree reached or recorded; the upper limit of variation.

The time or period during which the highest point or degree is attained.

An upper limit permitted by law or other authority.

The moment when a variable star is most brilliant.

The magnitude of the star at such a moment.

The greatest value assumed by a function over a given interval.

The largest number in a set.

Having or being the greatest quantity or the highest degree that has been or can be attained

Of, relating to, or making up a maximum

The highest limit.

(mathematics) The greatest value of a set or other mathematical structure, especially the global maximum or a local maximum of a function.

(analysis) An upper bound of a set which is also an element of that set.

(statistics) The largest value of a batch or sample or the upper bound of a probability distribution.

(snooker) A 147 break; the highest possible break.

A score of 180 with three darts.

A scoring shot for 6 runs.

To the highest degree.

The greatest quantity or value attainable in a given case; or, the greatest value attained by a quantity which first increases and then begins to decrease; the highest point or degree; - opposed to minimum.

Greatest in quantity or highest in degree attainable or attained; as, a maximum consumption of fuel; maximum pressure; maximum heat.

The largest possible quantity

The greatest possible degree;

The point on a curve where the tangent changes from positive on the left to negative on the right

The greatest or most complete or best possible;