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http://en.wikipedia.org/wiki/Upper_and_lower_bounds

in example it says that

"2 and 5 are both lower bounds for the set { 5, 10, 34, 13934 }, but 8 is not"

Why "2"? as 2 is not in that set.

Also,

at:

http://en.wikipedia.org/wiki/Supremum

in example it says that

"The "Supremum" or "Least Upper Bound" of the set of numbers 1, 2, 3 is 3. Although 4 is also an upper bound, it is not the "least upper bound" and hence not the "Supremum"."

Why? as 4 is not in the set of 1,2,3 but if for a moment I think that as 4>3 so it is the upper bound of the set which contains 1,2,3 then am I correct to say that 3 is the least upper bound ?

Thanks in advance.

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# Upper bound and lower bound

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