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Let B, ≤ be a partially ordered set and let C⊂ B with c Є C. Then the element bЄ B is an upper bound for C if c ≤ bfor each c Є C.

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Q: How do you define an upper bound of a subset?
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How do you define the least upper bound of a subset?

Let (B, ≤) be a partially ordered set and let C ⊂ B. An upper bound for C is an element b Є Bsuch that c ≤ b for each c Є C. If m is an upper bound for C, and if m ≤ b for each upper bound b of C, then m is a least upper bound of C. C can only have one least upper bound, and it may not have any at all (depending on B). The least upper bound of a set C is often written as lub C.See related links for more information.


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