what is least upper bound
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Least Upper Bound. Let be a nonempty set of real numbers that has an upper bound. Then a number is called the least upper bound (or the supremum, denoted ) for if it satisfies the following properties: 1.for all .
2. For all real numbers , if is an upper bound for , then
2. For all real numbers , if is an upper bound for , then
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Suppose SS is an ordered set, with EE as a subset of SS, where EE is bounded above. Suppose there exists an α∈Sα∈S with the following properties:
A) αα is an upper bound of EE.
B) If γ<αγ<α then γγ is not an upper bound of EE.
A) αα is an upper bound of EE.
B) If γ<αγ<α then γγ is not an upper bound of EE.
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Least Upper Bound. Let be a nonempty set of real numbers that has an upper bound. Then a number is called theleast upper bound (or the supremum, denoted ) for iff it satisfies the following properties: 1.
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The least upper bound of A is also called the supremum of A. It can be written sup(A) or lub(A). Sets with no upper bound have no least upper bound, of course. The set of all numbers is an example. The empty set has no least upper bound, because every number is an upper bound for the empty set.
if u need a example I will show u
The least upper bound of A is also called the supremum of A. It can be written sup(A) or lub(A). Sets with no upper bound have no least upper bound, of course. The set of all numbers is an example. The empty set has no least upper bound, because every number is an upper bound for the empty set.
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