That is not a proof but a generalised argument. The actual proof, for people who believe in Set Theoretical approach to Pure Mathematics, is a set-theoretic proof, not a tabular one.
Then again Set Theoretic approach is a problematic and controversial one. There are different schools of thoughts - logicism, intuitionism, Formalism etc. that try to establish Set Theory as the foundations of Pure Maths albeit differently and separately. Finitism, on the other hand, is a philosophy that rejects Set Theory and Infinities/real numbers etc. Sets have never been defined, there are certain properties(mistakingly called as axioms) which an object has to satisfy to be called a Set. This approach is awkward. Hence, most of the so-called proofs in Set Theory, Countability, Computability etc. must be taken with a pinch of salt. One solution is to move from Set Theory to Type theory.
Joshua Mathew I think this one is very important, not also does he cover the history to give some extra motivation for learning the concepts. He gives reasons for the importance of these concepts. Also, he is very rigorous. Mostly everything he covers is precise, which makes it easier for me to understand. Although people who are new to mathematics won’t benefit much from this playlist if they don’t know the intuition behind it. Like he said, this calculus course is for the ambitious.
While covering thr topic of countable set ,you mentioned that f is a function from N to M But by the definition of function every element of domain set have unique image ,but if i take M as a finite set ,will this satisfy the definition of function??
As there can be all type of natural numbers,so as there can be decimal numbers..When he found out some number not being equal to any of the numbers ,there must be a number which is equal to that because we are just putting a decimal sign before the large natural numbers to get decimal number.. I am not able to be intuitive in this case... Can anyone help please!?
I love this Professor. He's awesome.
That last proof's beauty blew me away!
That is not a proof but a generalised argument. The actual proof, for people who believe in Set Theoretical approach to Pure Mathematics, is a set-theoretic proof, not a tabular one.
Then again Set Theoretic approach is a problematic and controversial one. There are different schools of thoughts - logicism, intuitionism, Formalism etc. that try to establish Set Theory as the foundations of Pure Maths albeit differently and separately. Finitism, on the other hand, is a philosophy that rejects Set Theory and Infinities/real numbers etc. Sets have never been defined, there are certain properties(mistakingly called as axioms) which an object has to satisfy to be called a Set. This approach is awkward. Hence, most of the so-called proofs in Set Theory, Countability, Computability etc. must be taken with a pinch of salt. One solution is to move from Set Theory to Type theory.
@@kalyaninutopia Type Theory isn't a Axiomatic Theory?
SIR , your lecture is so good . can you upload your lecture notes ...this helps us more . thank you.
Visit nptel and open site and click course and search course name and download assignment and pdf
great sir realyy enjoy it.best ever
It is really a helpful lecture. I request you to give more lectures like this one . I like way your of teaching.
So much mathematical history covered and it makes me sad that I’m just learning these things :(
Brazilian?
Joshua Mathew no, American
@@JuanRodriguez-tr6st I was thinking to watch the whole series , is it nice?
Joshua Mathew I think this one is very important, not also does he cover the history to give some extra motivation for learning the concepts. He gives reasons for the importance of these concepts. Also, he is very rigorous. Mostly everything he covers is precise, which makes it easier for me to understand. Although people who are new to mathematics won’t benefit much from this playlist if they don’t know the intuition behind it. Like he said, this calculus course is for the ambitious.
@@JuanRodriguez-tr6st thanks mate.
How can i get the notes?
While covering thr topic of countable set ,you mentioned that f is a function from N to M
But by the definition of function every element of domain set have unique image ,but if i take M as a finite set ,will this satisfy the definition of function??
As there can be all type of natural numbers,so as there can be decimal numbers..When he found out some number not being equal to any of the numbers ,there must be a number which is equal to that because we are just putting a decimal sign before the large natural numbers to get decimal number..
I am not able to be intuitive in this case...
Can anyone help please!?
Can you annotate the time in which this is discussed? Thank you
@@JuanRodriguez-tr6st what!!??
@@sheetalmadi336 write the time in the video at which u had this doubt.
where can we get the notes sir is talking about
even im wondering that
Have you found
Sir please make some vedios lectures on nbhd open set closed set etc
where do i find the notes
Sir can you plz upload some questions and answers based on each chapter,?
Where i can find notes sir
#help
Is there lecture of point set topology? i need
excellent lecture...
Sir can u provide us pdf notes if possible because I m from UP and want to learn it more clearly,.
Plz sir if possible.