Hello sir.. I have no words to thankyou enough.. I am also a teacher but seeing you working so hard gives me all the more motivation to work hard.. P.s. -These lectures are savior for distance learning students.. More power to you.. Regards
Sir g ap great hain ap itna acha samjata hain k yakeen karain dil khosh ho jata ha 😍😍great love and respect from pakistan long live sir g hats off to you😍😍😍😍
The lectures are so simplified and one can very easily understand. The credit actually goes to your own depth pf understanding sir. You have cultured this topic very well.
Sir I am very happy to see this video......really this video is very helpful for me...... thankyou so much sir....thankyou so much......bas aap video dalte rahiye.... please sir ..
What if countability is inconsistent? The following is adopted from Mueckenheim: If the fractions m/n are enumerated by the natural numbers k according to Cantor's function k = (m + n - 1)(m + n - 2)/2 + m then all the fractions of the sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... are enumerated. But if the natural numbers first are in bijection with the integer fractions of the first column of the matrix 1/1, 1/2, 1/3, 1/4, ... 2/1, 2/2, 2/3, 2/4, ... 3/1, 3/2, 3/3, 3/4, ... 4/1, 4/2, 4/3, 4/4, ... 5/1, 5/2, 5/3, 5/4, ... ... then they must be distributed over the matrix such that no fraction remains without index. That means, there is a permutation such that the X of the first column XOOOO... XOOOO... XOOOO... XOOOO... XOOOO... ... by being exchanged with the O's cover all matrix positions. All O's will vanish. This is obviously impossible because exchanging cannot reduce them. The number of not indexed fractions, represented by O's, will remain constant forever, in infinity.
Thank you so much sir 🙏🌹🌹 aapne sb kitne simple way me explain kiya sb ek bar me hi smj aa gya mene or bi lectures dekhe but sb bol dete h ye similar h but explain nhi krte why so thank you sir again
Thank you sir... Bohott achaa padhaya hai aapne... Par mujhe samjh nahi aa raha hai ki hum yeh kar kyu rahe hai... Par koi baat nahi achaa lagaa aap se padhkar❤
Hello sir..
I have no words to thankyou enough..
I am also a teacher but seeing you working so hard gives me all the more motivation to work hard..
P.s. -These lectures are savior for distance learning students..
More power to you..
Regards
Thanku so much sir....
0
Have not seen anyone teaching so good. Nicely explained.
None can be compared to Nikhil Sir....He is THE BEST
Sir g ap great hain ap itna acha samjata hain k yakeen karain dil khosh ho jata ha 😍😍great love and respect from pakistan long live sir g hats off to you😍😍😍😍
Kitne simple way me countable infinite set smjha Diya sir aapne..🤔 pahli baar achhe se smjh aaya,🙏
Thank you very much sir great explanation as always ,and great representation sir 🌹🌹🌹🌹
Explained the concept in very simple language 👍🏻👍🏻
The lectures are so simplified and one can very easily understand. The credit actually goes to your own depth pf understanding sir.
You have cultured this topic very well.
Sir I am very happy to see this video......really this video is very helpful for me...... thankyou so much sir....thankyou so much......bas aap video dalte rahiye.... please sir ..
Sir bahuuut aaccha smj aaya..... Plss sir real analysis ki videos share kijiye....... Bahuut hi jyada helpful hoti hai........ Thank uhhh sir
Mind blowing sir....superb explanation and amazing representation sir...thank you so much...sir 🙏
Nice video sir🎉 and thank you
Love ur lecture sir the basics make our concept much clear
Very Informative and Helpful and Intersting lecture...👏👏👏👏
Super sir.mind blowing.itna acha pdate ho sb kuch clear ho jata h.kuch puchhne ki jrurt b nhi pdti again
Thank you sir for making this concept so easy to understand 🙏🙏😊😊
Awesome teaching sir 👍👍😄
What a great explanation I see ur three lecture series in the same topic thank u sir ❤
Thank you very much for clearing doubt which had not cleared upto now
What if countability is inconsistent? The following is adopted from Mueckenheim:
If the fractions m/n are enumerated by the natural numbers k according to Cantor's function
k = (m + n - 1)(m + n - 2)/2 + m
then all the fractions of the sequence
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
are enumerated.
But if the natural numbers first are in bijection with the integer fractions of the first column of the matrix
1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
...
then they must be distributed over the matrix such that no fraction remains without index. That means, there is a permutation such that the X of the first column
XOOOO...
XOOOO...
XOOOO...
XOOOO...
XOOOO...
...
by being exchanged with the O's cover all matrix positions. All O's will vanish. This is obviously impossible because exchanging cannot reduce them. The number of not indexed fractions, represented by O's, will remain constant forever, in infinity.
I am blessed for having taught by you, sir
Great sir 👌, please padhana band mat karna , app bahut achha padhate ho ,. 😄Thank you so muchhhhh....
Make a separate playlist on real Analysis bsc ...please Sir
Thank you sir your video is very helpful for basic concept.🙏🏻🙏🏻
The Best Explanation, Sir!!
Crystal clear lectures sir 🎉🎉🎉
Worth watching !! After watching all the videos of this playlist.
Kash yeh channel pehle mil gya hota toh kitna kuch seekh gye hote abhi tak
Thanks sir. Bahut acche se samach aa gaya. 😊🙏
Sir अच्छी तरह से समझ में आ गया thank you sir
Sir aapka samjhane ka tarika bahut accha hai. Thanx u sir
Thank you so much sir 🙏🌹🌹 aapne sb kitne simple way me explain kiya sb ek bar me hi smj aa gya mene or bi lectures dekhe but sb bol dete h ye similar h but explain nhi krte why so thank you sir again
Thank you so much sir for providing us a wonderful content 🙏🙏🙏🙏
Just amazing the way of teaching ❣️
thanku Sir bhut hi easy way pe aapne Etna achha samjhaya
Keep it up sir.
We really appreciate your hard work and efforts❤️love from assam
Outstanding lectures sir 👌 👏 👍
Than q sir🙏🙏
Thank u so much sir and also I want to ask why R is uncountable
Ekdam khtarnak sir ,thank u
Very nice lecture sir thank you sir🙏🙏🙏
Are sir mzaa AA gyaa ..lekin dimaag ki dahi ban gyiii ...fir bhi bhut enjoy kiye hai .....hm ISS ...countable set m .....bsttttt 😘😘😘🤗🤗🤗
Hi sir I have one query
Agar hame A~N show karna hai to Hamesha N -->A Mapping leni hogi kya
Ya hum A-->N define karenge to bhi chalega
Thanks a lot sir, Enjoyed watching your video.
World class teacher ho sir ap ❤
Thank you sir for providing such kind of video 🙏🙏
Thank you sir... Bohott achaa padhaya hai aapne... Par mujhe samjh nahi aa raha hai ki hum yeh kar kyu rahe hai... Par koi baat nahi achaa lagaa aap se padhkar❤
Now I am able to fight with real analysis 🙏🙏🙏🙏
Namsty sir ..this is very important vedio for me . thanks a lot 🙏
Sir aap bhut achha padate ho theoretical ko bhi esa gajab samajhate ho
Amazing explanation 👍🏻👍🏻
Sir brilliant teaching.....
Thank you so much sir 🙏🙏🙏🙏🙏🙏🙏🙏🙏 for making such an Amazing video 🙏
Sir please make videos all topics of real analysis& thank you so much sir
Excellent explanation sir 🙏🙏🙏
Great explanation. Thank you sir!🌸
It would be really helpful if apply these simplifying teaching techniques to Abstract algebra also☺️ btw great work.
Hello sir ,
sir how will we get to know that which function to use to relate between two sets in order to show them equivalent.....
In most cases they will give a function in question so from that we can check if it's equivalent or not ...
Sir superb explaination
Thank u so much ❤️🙏
Hello sir can you upload videos on iit jam preparation
Sir kuch previous years k question bhi karte rha kro her topics k liye.Thank u sir❤️
Thanku so much sir for this wonderful explanation 🙏
Best way to teach sir🙏🏻 book me to kuch samjh hi nhi ata h 😅
Excellent teaching and explanation sir..
Sir
How to prove set of real numbers is uncountable. Considering cardinality of rationals
@ignited minds
Very help full sir thank you so much
ab real analysis se darr nhi lagta
Thnku soo much sir...really ur videos are very helpfull🤗
Amazing sir..keep uploading
For any infinite set, there exists a bijection from the set to one of its proper subset.......is it true or false ??
Please ans me sir
Thank you very so much sir ☺️☺️
Thank you sir for helping us
Sir ,i did not understand the ordered pair of Q.
Sir most understandable ❤❤
Very nice explanation
great explanation ,sir
and thank u very much.....
Amazing sir keep uploading pls ...👍👍
Sir please make a video on squeeze theorem & Cauchy criterion in real analysis with some examples ...please sir
Splendid explanation
Awesome lecture sir 👌👌👌👌
Very nice explanation sir😊
Hello sir I HV 1 doubt
Z~N,
How can we define a function
You are so intelligent sir❤️
How can we write p/q in ordered format?
Thank you sir for B. Sc. Maths
Nice explanation Sir
Thank you so much sir finally countably infinite ka doubt clear hua 😍
*really amazing video!!*
Sir achha laga mujhe samajh mein aaya,and iit jam based pe bhi lecture daliye
Nice explanation sir thank you
You are great sir....
Excellent class sir
An awesome video and concepts 🤩
Really Nice Sir
Thanks for esiliye discussion sir.Again thank you.
Lovely video sir
Nice lecture, thank you
Very easy method to learn
Thanks so much sir ji
God bless you
Integer pe kese btayenge kon sa number 1 hai ????
Thanks a lot sir 💖
Sir best ever explained...I put messege please give me notes