# Dictionary Definition

minimum adj : the least possible; "needed to
enforce minimal standards"; "her grades were minimal"; "minimum
wage"; "a minimal charge for the service" [syn: minimal] [ant: maximal, maximal]

### Noun

1 the smallest possible quantity [syn: lower limit]
[ant: maximum]

2 the point on a curve where the tangent changes
from negative on the left to positive on the right [ant: maximum] [also: minima (pl)]

# User Contributed Dictionary

## English

### Etymology

From minimus### Noun

#### Antonyms

#### Translations

lowest limit

## Swedish

### Noun

minimum- minimum

# Extensive Definition

The largest and the smallest element of a
set are called extreme
values, absolute extrema, or extreme records.

For a differentiable function
f, if f(x_0) is an extreme value for the set of all values f(x),
and if x_0 is in the interior of the domain
of f, then x_0 is a critical
point, by
Fermat's theorem.

## Extreme values in abstract spaces with order

In the case of a general partial order one should not confuse a least element (smaller than all other) and a minimal element (nothing is smaller). Likewise, a greatest element of a poset is an upper bound of the set which is contained within the set, whereas a maximal element m of a poset A is an element of A such that if m ≤ b (for any b in A) then m = b.Any least element or greatest element of a poset
will be unique, but a poset can have several minimal or maximal
elements. If a poset has more than one maximal element, then these
elements will not be mutually comparable.

In a totally
ordered set, or chain, all elements are mutually comparable, so
such a set can have at most one minimal element and at most one
maximal element. Then, due to mutual comparability, the minimal
element will also be the least element and the maximal element will
also be the greatest element. Thus in a totally ordered set we can
simply use the terms minimum and maximum.

If a chain is finite then it will always have a
maximum and a minimum. If a chain is infinite then it need not have
a maximum or a minimum. For example, the set of natural
numbers has no maximum, though it has a minimum.

If an infinite chain S is bounded, then the
closure
Cl(S) of the set occasionally has a minimum and a maximum, in such
case they are called the greatest lower bound and the
least upper bound of
the set S, respectively.

In general, if an ordered set S has a greatest
element m, m is a maximal element. Furthermore, if S is a subset of
an ordered set T and m is the greatest element of S with respect to
order induced by T, m is a least upper bound of S in T. The similar
result holds for least element, minimal element and greatest lower
bound.

minimum in Arabic: حدود عليا وحدود دنيا

minimum in German: Extremwert

minimum in French: Extremum

minimum in Icelandic: Útgildi

minimum in Dutch: Extreme waarden

minimum in Polish: Ekstremum

minimum in Portuguese: Mínimo

minimum in Finnish: Maksimi

# Synonyms, Antonyms and Related Words

ace,
adequacy, adequate, adequate supply,
adequateness,
ample, atom, bare minimum, bare
sufficiency, barely sufficient, bit, commensurate, competence, competency, competent, corresponding, dab, decent, dole, dot, dram, dribble, driblet, due, dwarf, enough, equal to, exact measure,
farthing, few, fit, fleck, flyspeck, fragment, gobbet, good, good enough, grain, granule, groat, hair, handful, iota, jot, just enough, least, little, little bit, littlest, lota, lowest, margin, minim, minimal, minutiae, mite, modicum, molecule, mote, nadir, nominal, nutshell, ounce, particle, pebble, pinch, pittance, plenty, plenty good enough,
point, proportionate, reduced, right amount, satisfaction, satisfactoriness,
satisfactory,
satisfactory amount, scruple, shortest, slightest, smallest, smidgen, smitch, speck, spoonful, spot, substantial, sufficiency, sufficient, sufficient for,
sufficientness,
sufficing, suitable, thimbleful, tiny bit,
tittle, trifling amount,
trivia, up to, whit