🔶09 - Bound Set and Bolzano Weierstrass Theorem | Upper Bounds, Lower Bounds and Limit Points

🔶09 - Bound Set and Bolzano Weierstrass Theorem | Upper Bounds Lower Bounds and Limit Points

In todays video we shall be looking at the bolzano-Weierstrass theorem as well as the bound set.
A set S is said to be bounded above if there exist a real number say M, such that x is less than or equal to M, for all x is a member of S. M = upper bound

A set S is said to be bounded below if there exist a real number say m, such that x is greater than or equal to m, for all x is a member of S. b = lower bound

If the set S is bounded, then it has an upper bound and a lower bound.

Eg. If S = {5,6,7,8,9,10}

Upper bounds = 10,11,12,13.....
least upper bound = 10
Lower bounds = 5,6,7,8.....
greatest lower bound = 5

Bolzano-Weierstrass Theorem states that: every bounded infinite set has at least one limit point.

00:00 - Bound Set
06:03 - Example on Bound Set
10:47 - Bolzano-Weierstrass Theorem
11:31 - Example 1 on B-W-T
17:21 - Example 2 on B-W-T

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