Lecture-7|Every subset of a countable set is countable|Statement and proof|Countability|RealAnalysis

[@kabirkhan1488]

Thanks sir great explanation ❤️

[@thenewdimension9832]

Great ,best explanation 😍😍😍😍

[@kmrzeshuugaming1152]

NYC explanation

[@thenewdimension9832]

Please sir keep going , soon u will be on the top !

[@thenewdimension9832]

Sir plz make video on Every infinite set is equivalent to one of its proper subsets .

[@ima.pranjal]

You will get it soon.. maybe by tomorrow..

[@thenewdimension9832]

Thank you so much sir 🙏🙏🙏

[@nikhil8236]

find the limit points of the set: S=( 1, - 1, 3/2, - 3/2, 4/3, - 4/3 ,........)

[@laughtersite8308]

Sir last mai continuing this process we get, B does not equal to an1, an2, an3......

[@ima.pranjal]

Yes.. By mistake i wrote "=", it will be "≠"

[@nikhil8236]

@@ima.pranjal is it true proof??

[@maahinpanchal5828]

sir pls explain the example of real number is not countable in (0,1)

[@nisharawat20]

Sir yahan per n1 n2 n3 nk subsequence hogi bataiye sir

[@ima.pranjal]

Ha..

[@nisharawat20]

@@ima.pranjal okay acha sir suppose kare ki ham 2,4,6,7,8,10,12,14,,,,,,,,,,esa koi set ko natural number se equivalent dikha sakte hai kya

[@ima.pranjal]

Har subsequence me pattern find out krke map ko define krna bhot mushkil hota hai.. ispar researchs hote hai.. {2,4,6,7,8,10,12,14,....} ye subsequence to hai.. but iska map kaise define hoga ye research topic hai.. aur har sequence natural number ke equivalent hota hai.. to obviously {2,4,6,7,8,10,...} bhi natural number ke equivalent hoga..

[@nisharawat20]

@@ima.pranjal no sir ye subsequence kese hai kyunki 7 ko ap kese map ker payenge

[@ima.pranjal]

Natural number ka har infinite subset ek subsequence hota hai.

[@KORaju-nd7pt]

Please explain in English.

[@ima.pranjal]

I'll try to add the subtitles..