At 39:22 ,sir plz check ...4th option because continuous function maps interval to interval.Also inverse images of open set is open & inverse image of closed set is closed but direct images need not true.
Sir at 1:34:00 how can iii) option be correct because we are not given P(x) to X but rather between P(X) and X, so it can be true in ist case which implies iii) to be incorrect
Great sir everything you taught is just amazing. Sir I think only point set topology left by you,then you cover almost the whole syllabus. So sir please make video on that topic so it will help us a lot.
Sir at 9:47 in this qn can't we get infinitely many values of a,b,c in choosing different values of alpha,beta,gamma? Like you chose a specific case (1,0,0) which gave singleton, can't there be more possible alternative values to solve this qn? Kindly clarify. Open to understanding.
sir 1:35 p question h jisme disjoint subset dundne h jo dense ho but vo saath m countable bi hone chaaiye to aapne irrational ka set kyu consider kiya usme???
Sir u r telling if f cont then open set ki image open ,closed set ki image closed ,connected ki image connected or compact ki image compact ....but sir open & closed k liye to inverse image valid hoti h ...direct image thode hi ...correct me if m wrong ..
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Very helpful.... Keep it up...
Thank you sir for this content to develop my confidence
This is very helpful and enjoying session to understand cordinality topic
It's amazing ❤❤How can you explain all the questions easily? Best teacher ever... Please continue....
Outstanding sir.....very helpful sir❤
44:00 the cardinality of R and R^2 is same and there is bijection map
At 39:22 ,sir plz check ...4th option because continuous function maps interval to interval.Also inverse images of open set is open & inverse image of closed set is closed but direct images need not true.
Yes, it is correct.... Only inverse image is open.
. please rectify.
amazing content sir
first view awsome sir thnk uu so much💗💗💗
This is very helpful thank you so much
Very helpful vedio
Amazing work and Thank you so much sir , I learnt so many concept from your videos 🙏🙏🙏
Good job sir
Absolutely gorgeous lecture 😊
Thanks sir yu make easy for us ❤
1:20:39 sir cardinality of any power set can't be countable. Cardinality of a power set can either be finite or uncountable
Finite is also countable
Cardinality of any power set can't be countable infinite or denumerable.
Sir at 1:34:00 how can iii) option be correct because we are not given P(x) to X but rather between P(X) and X, so it can be true in ist case which implies iii) to be incorrect
Great sir everything you taught is just amazing.
Sir I think only point set topology left by you,then you cover almost the whole syllabus.
So sir please make video on that topic so it will help us a lot.
1:16:49 how the second option discards. The union of an uncountable set is uncountable!
The product is countable as it's product of finite sets
Very nice vedio sir🎉🎉🎉❤❤❤
Very thank you sir अब मुझसे भी question solve होने lga hai again thanks sir
बहुत अच्छा लगा सुन कर... ऐसे ही देखते रहे और सिखते रहे वीडियो से.. एक दिन सफ़ल्ता कदम चुमेगी..
Very very nice explanation sir ❣️thanks Sir 🙂
Your videos give me lot of confidence.....
Grate work sir
Sir at 9:47 in this qn can't we get infinitely many values of a,b,c in choosing different values of alpha,beta,gamma? Like you chose a specific case (1,0,0) which gave singleton, can't there be more possible alternative values to solve this qn? Kindly clarify. Open to understanding.
If u open the p(x) in set S u will gate uniqe value of abc zo that cardinality of Set S is 1..!!
Sir complex analysis, linear algebra and real analysis me jo important hai csir net k liye, please upload video
Already uploaded....kindly visit the channel
Kha se preparation kr rhe ho aap?
thank you so much sir 🙏🙏🙏
Thank you so much sir very helpful
Nice session....❤
Thanks you sir aap great ho
Thank you so much sir for uploading this video 🙂
Thanku🎉...very good vedios .
44:44 Sir, cardinality of R and cardinality of R^2 is same . So option C is correct.
R^2 to R me kya injection map possible ha ?
Thanks a lot Sir
Thankyou very much sir for your efforts 😊
50:47..
I think co domain of f is R as it is mentioned as real valued. Y is the set of pre images of 0 by f
Sir in 1:36:00 they are asking for countably dense subset.,irrationals are uncountable.
I also have the same query.
I think we can make countable set like c=Q+alpha
1:33:39 a,b,d option correct because x to p(x) me dakna ha
thank you sir.. plz upload some more pyq on important topics..
Super duper sir ❤❤❤❤
Nice explanation sir
Nice sir
Very helpful sir
At 1:36:22 how are you jusifying countability of Q^c (set of irrationals). It is uncountable.
Yes it is uncountable..
Yes
Thank u sir🎉
45:48.. Dec' 2020
Sir cardinality of R and R×R are same..
you put cardinality of R×R as c^c it should have c^2..
CAN YOU PLEASE VERIFY ONCE
Ya I also think
So helpful
Sir in last second question option c is right.. because w,X,Y, has cardinality C but Z has cardinality C^C
🎉🎉🎉🎉🎉🎉❤❤❤❤❤thank you sir
Jo Bach ja rha h ❤❤❤ sir use v upload kr dijiye plzzzzz and you are the greatest mathematician 🎉🎉🎉🎉
Thnku so much sir😊
Sir, your videos are really useful. Can u do pyqs like this for Statistics. It will be a huge help.
Many are already uploaded... check at my channel
Excellent
39:24 c Option nhi hoga kueki R is open but unit circle is not open
Only d option correct 😊
Thank you sir❤
Thank you sir 🎉
Sir (1) f(x)=x^2 on (-1,1) image =[0,1) not open hence every cts map does not map open to open
(2)how cardinality of R and R^2 different
Good video sir
1:36:20 how can all options be correct, because it's given that each if which is countable. Sir I think your answer isn't right there
Yes , set of irrational numbers is uncountable
Sir linear algebra full lecture marathon with concept clarity
12:00 sir in this question in option 1 p and q belongs to N not Q, so may be its uncountable
Kindly explain the concept of cauchy integral formula and residues, poles of function in detail with gate ,net and jam problem 🙏🙏
Already uploaded... Check PYQs on Residue, PYQs on complex integration lectures etc at my RUclips channel.
45:46 D is wrong answer. There do exist bijection ftom R×R to R.
sir 1:35 p question h jisme disjoint subset dundne h jo dense ho but vo saath m countable bi hone chaaiye to aapne irrational ka set kyu consider kiya usme???
Thankyou sir
39:24 in fourth option domain is compact set but {0,1} is not compact... So the answer is c only. Why d sir??
{0,1} is always closed and bounded,
So, compact hoga
@RanjangamingYT7477 closed interval [0,1] is closed and bdd. But this is points 0&1. How it is compact? I didn't understand 😇
@@dreamgirl61196 bounded and limit Point phi hoga
Look sir ne jaise bola that disconnect set maps to disconnect under CTS map
Please upload more video
Sir please make video on continuity and differentiability
sir 1:28 p jo sum h usme vo cardinality 100^100 kaise hui sir???
Upload video all topics Real analysis
Sir plz provide pyq series on abstract algebra
Sir ka domain nahi h yeh subject.. Kitne bar bola to h sir ne
🎉thank you sir ji please upload remaining concepts based video for csir net
Sir every continuous map open ko open pe kaise map kr skta h??
Counter f(x)=x^2 on (-1,1) image = [0,1)
√(1/n^2)-x^2 is really a rational no if this no is not perfect square
Sir please take singularity residue topic for csir pleaseee
Wow
Sir at the very beginning you say that if f:A to B is 1-1 then |A|
How can underroot of a no is rational no if this no is not perfect square
Sir u r telling if f cont then open set ki image open ,closed set ki image closed ,connected ki image connected or compact ki image compact ....but sir open & closed k liye to inverse image valid hoti h ...direct image thode hi ...correct me if m wrong ..
Yes u are right
Continuous image of connected set is connected and continuos image of compect set is compect hota h
Yha R me interval connected hote h isliye ye use kr skte h
ase or video for other topics
Abstract algebra short cut csirnet Dec 2023
Sir ka domain nahi h yeh subject.. Kitne bar to bola to h sir ne
Sir please upload some videos related to statistics
Already uploaded many and topic wise also
Thanks ❤
X is countable or Y is uncountable hoga sir right ans
Set of irrational is countable or uncountable?
Uncountable
Sif pls clear one thing about cts direct image of open closed may not be open closed
Yes, it may not open.... Only image inverse is correct.
@@DrHarishGarg ok...thanks sir...for clearing it.
Sir plzzz Hindi bhi use Kiya kro
Thoda sa sahi padaya kro
Galat salat concept bta dete ho
Sir please explain in hindi
LPP
In 10:03 for different choices of alpha beta and gama different (a,b,c) we will obtain then how is the set s contain only one element
Dear ... Kindly read the statement again ....Remember..We will always get unique a,b,c for choices of alpha, beta and gamma..... Thats why
@@DrHarishGarg thank u sir for solving the doubts. You're a life saver ❤️
Thank you so much sir🙏🙏🙏🙏🙏
Very helpful sir
Thanks sir❤
Very helpful sir