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Real Analysis

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The supremum of a set is the least possible upper bound of the set. The supremum need not be in the set.

The maximum of a set is a number which is an upper bound of the set, i.e. , . The maximum must be an element of the set.
As a result, some kinds of sets such as open sets don't have maximums. All finite partially ordered sets have maximums.

QuantumJG:
What does the standard topology of a metric space mean?

kamil9876:
The usual toplogy on a metric space is one where the open sets are those sets that are the unions of open balls, along with the empty set.

dcc:

--- Quote from: QuantumJG on March 13, 2010, 04:30:28 pm ---

Approaches 2.25 as n is this right?

--- End quote ---

Not sure if its still relevant, but you should be able to recognise this sum as a relative of the Geometric series - Consider the derivative of .  (Have you learnt about uniform continuity and power series?)

edit: fixed sum index.

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