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minimal and maximal number∗
pahio†
2013-03-21 17:47:52
Let’s consider a finite non-empty set A = {a1 , . . . , an } of real numbers or
an infinite but compact (i.e. bounded and closed) set A of real numbers. In
both cases the set has a unique least number and a unique greatest number.
• The least number of the set is denoted by min{a1 , . . . , an } or min A.
• The greatest number of the set is denoted by max{a1 , . . . , an } or max A.
In both cases we have
min A = inf A,
max A = sup A,
min A 5 x 5 max A ∀x ∈ A,
where inf A and sup A are the infimum and supremum of the set A.
The min and max are set functions, i.e. they map subsets of a certain set to
R.
The minimal and maximal number of a set of two real numbers obey the
formulae
a+b |a−b|
min{a, b} =
−
,
2
2
a+b |a−b|
max{a, b} =
+
,
2
2
max{a, b} − min{a, b} = |a−b|,
max{a, −a} = |a|
∗ hMinimalAndMaximalNumberi
created: h2013-03-21i by: hpahioi version: h36118i
Privacy setting: h1i hDefinitioni h26B12i h03E04i
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