Math Span

https://youtu.be/-HgSuY4FrHI

Inf(A)=-Sup(-A) / sum and product of rational and Irrational number is irrational number.

https://youtu.be/lpygMi7iVFo
Supremum and Infimum of a non empty subset of ordered set if exists is unique. 👇

Supremum and Infimum of a non empty subset of ordered set if exists is unique.

If A={ p : p€Q ^ p>0 : p²

If A={ p : p€Q ^ p>0 : p²

Set of positive rational numbers whose square is less than 2 contains no largest number. Proof

B={p:p€Q^p>0:p²>2} has no smallest number....
an important question of real analysis in an easy way
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Positive rational numbers with squares greater than two contains no smallest number. proof

If A={p:p€Q^p>0:p²0:p²>2} then A has no least upper bound and B has no greatest lower bound in Q.

Important Theorem of Real Analysis / Sup / Inf

https://youtu.be/egmCOZFP8iM

Upper limit topology on R is totally disconnected space /proof

https://youtu.be/JWwOG38UHCk

Prove that collection of all epsilon balls is basis for topology on X.

https://youtu.be/YLLDQpAd9ig

Topology/Constant/Inclusion/Continuous functions are continuous

https://youtu.be/xITFmjpsMUM

Every closed subspace of compact space is compact

https://youtu.be/hD3ZtJlD7I0

Image of connected space under continuous map is connected

What is the solution?