Sir, if A is countable. We also need to prove 1=>2 and 1=>3 for case when A is finite. and since every finite set is equivalent to some subset of natural number, we need to take B=A and C=A . Is it right?
@@this.is.me.obviously If A is finite it will be numerically equivalent to one of the subsets of N that is Jn ( from previous videos). So we can take B and C as Jn. Hope this is clear.
Sir, your way of clearing the concept is very nice! Thanks a lot for this help..Sir, if its possible discuss some problems related to NET..It would be very helpful for csir-net aspirants
You're right in that the correction is mistakenly saying the same thing as on the whiteboard. But keep in mind that from a mathematical perspective, both work. Whereas "A is countable" might be more general, it includes finite sets which meet the properties trivially. So "A is countably infinite" is more clearly an interesting statement.
@@cristianvaccarella8649 There is no need for a set to be finite in order for 2 to imply 1, or 3 to imply 1. The theorem that states that every subset of the set of natural numbers is countable applies to both finite and infinite sets?
It depends on what you are looking for and what your experience is with proof writing. Apostol is easier than Rudin for beginners but Rudin is a standard book and should be read by anyone interested in pure mathematics.
Yes. The first statement should have been "A is countable." Thank all the viewers who have pointed this out.
Sir, if A is countable. We also need to prove 1=>2 and 1=>3 for case when A is finite.
and since every finite set is equivalent to some subset of natural number, we need to take B=A and C=A . Is it right?
@@this.is.me.obviously If A is finite it will be numerically equivalent to one of the subsets of N that is Jn ( from previous videos). So we can take B and C as Jn. Hope this is clear.
I am understanding it very easily .. best teaching. I like real analysis
Sir, your way of clearing the concept is very nice! Thanks a lot for this help..Sir, if its possible discuss some problems related to NET..It would be very helpful for csir-net aspirants
God, give me the understanding power like this student sitting in front corner 31:06
:D
34:28, that stare into the camera is hilarious!!😂
amazing video sir, our prof is so shit we don't understand anything, you are a life saver.
I think the correction at 18:18 should read "A is countable" instead of "A is countably infinite"?
You're right in that the correction is mistakenly saying the same thing as on the whiteboard.
But keep in mind that from a mathematical perspective, both work. Whereas "A is countable" might be more general, it includes finite sets which meet the properties trivially. So "A is countably infinite" is more clearly an interesting statement.
Yes but if you consider A being countably infinite then 2 doesn't imply 1, nor 3 implies 1
Ah yes!
Cristian Vaccarella
correct argument therefore they fail to be equivalent
@@cristianvaccarella8649 There is no need for a set to be finite in order for 2 to imply 1, or 3 to imply 1. The theorem that states that every subset of the set of natural numbers is countable applies to both finite and infinite sets?
Is mathematical analysis by Rudin better or Apostol better ?Any suggestions ?
It depends on what you are looking for and what your experience is with proof writing. Apostol is easier than Rudin for beginners but Rudin is a standard book and should be read by anyone interested in pure mathematics.
very nice
thnx a lot sir for giving us a great help
Can anyone please tell me the meaning of 'Mod' in the captions of these videos? Thanks.
Module
Made it to lec 4
good class thanks sir
8:35 1=2 confirmed
Aap pathate hi Es se bathkar Kya ++what