🔶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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[KhadijaKamil-eljs]

Please, for the last question, why is the set closed

[baklash]

Can you have recap sessions where you just solve different types of questions please

[samueladdai]

Please can you make videos on sequences

[evanstwedeer]

Also, why is that 1 is not a limit point of set S? Neighborhoods of 1 intersection S has many points but you didn't include it.
You just took 0

[kelvinkwawafful]

In the last video why is the limit 1 and not 0

[evanstwedeer]

Please why is the l.u.b. for set P not 1?🤔

[emmanuelarthur]

Great video. But I didn't quite get the last example .I understand why the set SB has a greatest lower bound of 0.9, but can you please explain to me why the set SA has a least upper bound element of 1.1.Since the set is approaching infinity must not the greatest element be infinity

[teenamorrison]

The limit point is where the set approaches right?
and infinity is like saying the set never ends, am I right?
If so, how do the sets have a limit point but still called infinite?

[asaredurowaadoris]

pls wat if the interval given is an open interval like (0, 4), will it have upper and lower bound

[Novatron]

can you do videos on electrical
machines

[KhadijaKamil-eljs]

Please, for the last question, why is the set closed

[KhadijaKamil-eljs]

Please, for the last question, why is the set closed