To prove dense B(x,r) intersection S is non empty. S=Q intersection [0,1] is a countable set. and subspace topology

Nice - exactly what I needed for my University. Thank you so much!

Sir, rank (AB)<=min{rank A,rank B} So, rank (AB)<=min{m,m} as m<n. So rank (AB) = m and order of AB = m*m so rank AB= min{m,m}=m. Det (AB)≠0 . Hence non singular. And rank (BA)= min{rank B,rank A} = m. And order of BA=n*n so rank (BA)= min{n,n}= n . And m<n. So det(BA)=0. Hence singular.

Sir, I have doubt after 14:25 could u recheck it pls

finally understood thank you sir….this was asked in my university exam

Very interesting 🎉

Beautiful explanation

Nice one sir. As you said this is helpful in other problems also..❤

Sir , Make more and more videos sir, its like your one question solving video equals minimum 5+ new and unique ideas. This is helpful in solving other problems. Always A great fan your teaching.

Thank you so much Sir

Wonderful ❤

You are videos are really really helpful sir. Its like whenever I get bored of studying I start to watch your videos and it is really a boost up . as I am learning lots of information from a single question itself. ❤

Sir, one doubt, to see whether f(x) is differential or not.. . We have to check for the diff at 0???? How do we check that sir. Why are we checking only the x eq 0 case only

Super Sir.. thank you so much.

🙏

how u can use dominating convergence theorem

Thank you sir

I couldn't have done it without you.🙏

Tq u so much it is very helpful

Nice explanation

i am trying i dont know whether i will pass or fail but will try best

What's the final answer ? Is it 3?

Very lengthy 😏

Generally what is an induced map?

good

Sir please continue uploading videos , you give detailed solution .

I went here from character ai.. Thank you sirr

I found you very recently in you tube and become a fan of yours teaching...you are such a wonderful teacher and your way of making one understood is phenomenal.Thank You

Sir, for showing unboundedness in option d can we take {(z,w): z=sqrt(n + 1) and w= sqrt( n ) for some natural number n }

🎉 great clarity. Such easy explanation. Thanks

Pi( a0,a1,a2,a3,a4,a5)=a0+a4? Is projection map continuous?

Is this in any text book

How closed [0,1] is equal to finite union of U beta i's

Will it contradict CLT if we take for 2+2 cylces instead of 3 cycle

Will it contradict CLT if we take for 2+2 cylces instead of 3 cycle

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Thank you sir for giving hints to get clear idea by framing with examples sir.

Thank you so much sir, Clearly explained sir.

Sir apka phone no dijiye

I'm not able to find the lemma in my book. please share the source you get it from. Please.

Thank u so much anna 🔥

You are the best sir.. I always hate when this kind of concepts are explained in hindi.. Your channel is a gem.. I understand the concepts well.. Thanks

Splitting field of x^2 + 1 is Q(i)..isn't it?

Your a saviour brother ❤️

Nice video sir👍

Nhi aya samajh me

Sir upload videos gate 2023 regarding

Sir gate 2023 ke regarding videos banaye sir

Your explanation is very good. Do check our content also, we are also creating quality content in Mathematics

Thank you sir