Bolzano Theorem || Real Analysis || Continuity || Lecture 20 ||

[@Brain_Games01-m9j]

Well explained sir 👏 thank you so much 🎉

[@khushi15711]

Thank you so much 🎉🎉🎉keep doing...👍👍👍

[@RahulSaini-zk4bh]

Thanks sirji well explaination

[@yashsharma5896]

Appreciate your good work sir

[@qurat-ul-ainsher6641]

Thank u so much really very informative vedioo.

[@sayanjitb]

If b-delta >c and f(b-delta) >0 then b-delta is inside the set S. Then how can c be the supremum of set S? Doesn't it contradict with our assumption? Timestamp 15:53

[@dipenderyadav98]

F(b)

[@akshaychopra6679]

Bade dino me aye sir g. Miss kr rhe they apko

[@mathmavens6215]

Having some internet connection problem, will try to fix it soon.😉

[@akshaychopra6679]

@@mathmavens6215 ok sir g

[@PreetiYadav-ng1kw]

Thanks 🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🕉🧡🕉🕉🕉🕉🧡🕉🕉🕉🕉

[@CBI_0966]

Kya ye answer exam me likh skte hai sir plzz reply❤

[@mathmavens6215]

100 percent 👍

[@CBI_0966]

@@mathmavens6215 thanku sir 🙏🏻

[@hemrajprajapat97]

Sir sign retainment property ko Hindi me kya khte h

[@mathmavens6215]

चिन्ह संरक्षण संपति

[@phonetricks31]

Sir ye samaj nahi aaya

[@RajitaRaj-bw8mr]

Limi continuous bhi bta dijiyega vo bilkul bhi nhi samjh me aata hai

[@mathmavens6215]

Sure

[@abhi7497]

sir in case of f(b)

[@mathmavens6215]

c is supremum of set S and in set S we are collecting all those x which are greater than or equal to a and strictly less than b, where f(x)>0 then we are saying that C is sup of set S.
Maybe you are considering c to be supreme of (a,b) that's why you got confused. Also, b is not attaining negative value. The function f is negative at b.
I hope it's clear now !!

[@AbinayChamlingVlogs]

❤

[@CBI_0966]

Kyya ye answer exam me likh skte hai❤

[@mathmavens6215]

100 percent 👍

[@LearnerForlife-fk2cp]

Sir I am preparing for jee advanced, i came to see bolzano theorem ( though only initial part of this lecture was relevant for me )
But it helped a lot 😁
Thank you sir

[@mathmavens6215]

All the best for exam.

[@Parth14b]

I really hate when people bring another theorem to a specific theorem

[@mathmavens6215]

This is the beauty of Mathematics ❤️ Everything coming together to prove certain results shows us the power of unity😉

[@successiswaiting_997]

Kya baat h ​@@mathmavens6215

[@parthsarkar1760]

Mujhe kuch samaj nehi aya

[@PreetiYadav-ng1kw]

Thanks 😍😍🕉🕉🕉🙏🏼🕉🕉🕉🕉🕉🕉🙏🏼🙏🏼🙏🏼🕉🕉🕉🕉🥰🥰🥰🕉🕉🕉🕉🕉