# Lecture 1 – Real Number

### 92 thoughts on “Lecture 1 – Real Number”

• February 11, 2008 at 5:09 pm

can you give the lectures in a sequence ?..because it is hard to know which is lecture 1 and so on…..

• February 12, 2008 at 5:39 am

Please view the playlist titled 'Mathematics in this channel for the complete lecture series in a sequence. Note that the lecture number is given in the description of the video.
Thanks

• March 11, 2008 at 5:44 am

Good video – thanks! You might want to take a look at 41:00; there is a technical glitch there where the writing doesn't appear.

• March 11, 2008 at 5:54 am

Excellent summary of the basic properties of Real numbers and how they are derived as well as why they are important. Thanks again!

• September 13, 2008 at 12:49 am

Pertaining to 13:57. All he is saying is that if we can show there exists some n such that (2r/n + 1/n < 2-(r^2)) then it would follow that 2r/n + 1/(n^2) < 2-(r^2) since 1/(n^2) < 1/n. He ends the proof with an appeal to the Archimedean property to show the existence of such a n.

• October 11, 2008 at 7:07 am

Great lectures except that I can't read the darn thing. Too bad.

• February 3, 2009 at 8:10 am

I think you mis-understood it. He says that if he can find an 'n" such that Y<Z is satisfied, then automatically X<Z will be satisfied. Hope it clarifies.

• February 14, 2009 at 11:27 am

how is this relavent to calculus this is not calculus calculus is about functions people already know about natural rational numbers etc

• March 22, 2009 at 6:01 pm

really good video with good explanations but I couldn't read the handwriting 🙁

• March 26, 2009 at 2:12 pm

It is not possible to understand advanced calculus or complex analysis without understanding the structure of real numbers & analysis.
However, most of the calculus they teach constitute, application of formulas, few fundamentals, substitutions, logical steps, finding similarities & parallelalities.
Unfortunately, this & other presentations by Dr. Ray is not visible.
I urge him to present a clearer & visible version of his lectures.
Also, please give more examples on the number line.

• April 12, 2009 at 5:32 am

and 1/3 is between 1 and 3.

• April 12, 2009 at 5:21 pm

Embarrasingly inept. Why bother videoing these lectures if 1/2 our time is watching Prof Ray writing indecipherable symbols on his acetate. He should have referred to pre-printed & readable lecture notes !!
Much better to read a textbook – this is a tortuous & deeply inefficient way to learn Calculus.

• April 13, 2009 at 3:46 pm

please read :"what is mathematics" book then you will come to know the importance…..

• April 25, 2009 at 12:30 am

It has nothing to do with depth. I am referring to his pedagogical style. Amongst the worst I have seen. Complete geek unable to communicate or inspire. And wretched handwriting.

• May 6, 2009 at 2:02 pm

It was funny, but i'm not sure it's meant to be.

• May 19, 2009 at 1:30 pm

Ref: 16 to 17 minutes
In simple words, he is saying, between any two different real numbers, no matter how close together, there are infinitely many other real numbers. So there is no number larger than any number on the real number line or no number smaller than any number on the real number line

• May 20, 2009 at 9:49 am

Forget waterboarding, we have a new form of enhanced interrogation!

• July 1, 2009 at 10:35 am

guys is there a trancript of this lesson. He is a good teacher but his accent is killing me 🙂

• July 2, 2009 at 2:21 pm

For real number do you mean rational plus irrational?

• July 4, 2009 at 5:45 pm

Need help guys: Why does he introduce te relation 1/n2<1/n. I agree on the values but I don't see the logic of it.

• July 7, 2009 at 7:10 am

Nice teaching and the Kolkata accent was nice as well! Just one small correction at around 52.00 where he says any S which is a subset of R has a supremum. It should be any S which is bounded above has a supremum. For e.g N which is a subset of R does not have a supremum.

• July 15, 2009 at 9:39 pm

strangely I can understand his writings but not his vocalisation. But I don't despair I'll get used 🙂 HAs someone post some notes of the course?

• July 29, 2009 at 11:29 am

go to the nptel website , you will find a web course there too.

• October 15, 2009 at 3:29 am

Yes, download them, open them in a movie editing program, and slow it down by a factor of like .9 or so 🙂 You can download them using DVD video soft.

• October 15, 2009 at 3:47 am

You must be in a very advanced high school 🙂 I learned some of this in my grade 12 (America), and have extended these ideas in my freshman year of college. My masters degree doesn't include this because it will already have been covered 🙂 More advanced/addictional topics will be covered than real and complex analysis.

• November 8, 2009 at 7:18 pm

whats hee sayingggg
!!!!!!!!!!!

• November 26, 2009 at 5:45 pm

It's not that hard to understand him or any of the IIT professors, just focus on what he is saying more. I have had 2 teachers with a heavy accent, so I guess I have gotten used to it

• December 19, 2009 at 1:57 am

some people are so ungrateful. the lecturer is taking his valuable time to teach us for free but instead of being thankful, some viewers have nothing but negative things to say.

if you are getting a high paying job opportunity to work abroad or in a global company that deals with multinationals, would you turn it down or would you accept it and adapt to the accents?

please stop being so closed minded. if you cannot understand him, pause and play back but don't be negative or insulting.

• December 22, 2009 at 11:37 am

HEY VIEWERS…Prof Ray is great but i fond another professor who is EXTREMELY GOOD when it comes to teaching CALCULUS if you are interested. copy and paste the following. trust me you won't regret it!……

Calculus1 Lecture1

or if you are doing college algebra….

College Algebra – Lecture 1 – Numbers

you won't regret it!

• January 27, 2010 at 11:59 am

Good and clear explanations.

But please see if you can improve the quality of the writing. The images are not very clear. If the visual form is good it is much easier to focus on the content.

• January 30, 2010 at 6:14 pm

This course is the equivalent of Calculus II & III right?

This course looks as if it will drop heavily off the deep end very quickly…

• January 30, 2010 at 6:23 pm

Wow, I never understood the contradiction in the proof of root 2 being irrational!

This guy is good :p

• April 10, 2010 at 12:21 am

@ ebunny5 we care and appreciate the proffs time only if it values us!!!! He is just an amazing guy in knowledge, but in teaching with the greatest of heart i could give him 35%. Students need real teachers not anybody else!!!
@alexlaur2007: listen we care a lil bit of the guy's accent since it deals with our understang and nothng more!!! If I am a real student i would personally give nothing towards his english if i understand him!!!! But the prob he complicates things thats all!!!!

• May 10, 2010 at 3:25 am

Ref [54:12] Archemidian Property Application (1): (small typo)

I think you meant (1/n < eplsilon) not the other way. (refer [35:16])

BTW: Love the lectures. Keep up the gr8 work

• July 10, 2010 at 7:59 am

I had this confusion for l.u.b always but after after this lecture everything is very clear thanx a lot

• August 6, 2010 at 7:50 am

Great video!

• August 8, 2010 at 11:21 pm

@pablito12sc lol

• August 26, 2010 at 1:15 pm

Very important basic proof at 10:20.

Does the set B = {q: q^2 <2 } contain a largest member? Nice job. Simple and clear.

• September 25, 2010 at 3:11 pm

I am not abl to express my gratitude to thes lecturers.They even explain even the minute concept with great simplicity.Thanks youtube..I wud also thank these lecturers.Regret that i had not thought of this before………….

• November 8, 2010 at 8:59 pm

Thank you so much for this lecture sir. I am most grateful.

• December 2, 2010 at 10:12 pm

8:33
There is an error with the representation of the number 1/2 on the line. It should be between 0 and 1, but it is shown to be between 1 and 2 in the video.

• May 12, 2011 at 10:05 pm

I think at 10:20 he's trying to prove that the rationals don't have the completeness property; e.g. he takes a particular set of rationals and shows that it is not bounded above. He also states that this particular set is not bounded below, although he doesn't actually﻿ prove it.

• May 24, 2011 at 3:52 am

Thanks for the lecture.

• June 10, 2011 at 8:06 pm

@chpsanders
friend rationals are surely bigger set than integers because consider 3. 3 is an integer and at the same time rational _can be represented 3/1 which makes it rational……….

• July 15, 2011 at 11:17 am

Negative Natural numbers ??

—- but aren't natural numbers the ordinary counting numbers 1, 2, 3,…
(or)

is it that there is no universal agreement about which set of numbers is designated by the term "natural numbers"!!

• July 21, 2011 at 5:10 am

@psycool666, Math is a language and not just a way of solving problems. In mathematics sometimes you have to define very specifically what you are describing. sometimes it is convenient or necessary to bound natural numbers as all integers greater than or equal to 1 sometimes you need to describe natural numbers as all integers, sometimes all integers other than 0 is useful. it depends on what you are describing. you could say Alaskan winters are cold. or the killer was cold.

• October 5, 2011 at 9:20 am

Video is not clear

• December 24, 2011 at 2:55 am

thanku sir.

• January 9, 2012 at 2:05 pm

If anybody is to grumble, it is about the quality of the video youtube provides.

• January 12, 2012 at 1:12 pm

@psycool666
Negative natural numbers doesn't mean the negative part of the natural numbers. It means the negatives of the natural numbers. Also, names are nothing but convention, and at least in India we call the set of negative numbers the set of negative natural numbers,

• January 12, 2012 at 2:18 pm

I Really Like The Video From Your Lecture 1 Real Number

• January 14, 2012 at 10:53 am

@ls600h1

I'm sorry If I sounded Cocky actually I'm a non-math student, and have been interested in math after my college, so a lot of self learning, It is just that these terms are a bit Confusing , Cuz I read that the number "1" was the lowest Natural number, and I definitely don't doubt on what an IIT professor is lecturing on – Cuz Im from India too, maybe it is just that these Terms aren't STRICTLY DEFINED to apply them Universally

• January 16, 2012 at 12:24 pm

@psycool666
Well your version of the definition is correct, and the smallest natural number is 1, but what I think the lecturer meant was the negative of natural numbers, so basicly its the set of elements -x, where x is an element of natural numbers

• January 17, 2012 at 2:23 am

@ls600h1
But wouldn't set of " Negative INTEGERS " would have fit well rather than set of negative of natural numbers as INTEGERS already contain them as a part of their Complete Set – It is just that it is less confusing where we mention a SET which is already a part of it instead of Creating a Set that isn't actually there

• May 2, 2012 at 5:10 am

nice lecture!

• October 17, 2012 at 4:15 pm

awesome video…………….

• November 16, 2012 at 1:28 pm

WHY MUST I BE SO INEPT AT MATHEMATICS!? fuck i go to the most basic maths video on youtube and the first thing he says confuses me and i can't focus anymore. fuck!

• December 11, 2012 at 12:54 pm

Thank you to the government for such a greatest idea to make this type of lectures… from lectures…………….

• January 6, 2013 at 4:27 pm

lots of bayans from 12:03 and on

• February 3, 2013 at 10:29 pm

Where do you live? I don't know of any country in the world where this is 7'th grade material…

• May 7, 2013 at 3:06 am

Do you really understand these concepts in 7th grade ? Do you really understand what analytical functions are ? I certainly did not.

• May 20, 2013 at 9:52 am

wow!! this is a very good idea and i wish other countries in the world would adopt this.

• September 14, 2013 at 9:24 am

I want video lectures of topology of metric spaces by
Professor S K Ray plz mail me the link

• October 15, 2013 at 5:45 pm

dont try to see the starting concepts ..they are just the intro …see the ending of the playlist and then compare your 7th grade concepts with IIT…Seems as if you are another creep not getting into iit's !!!

• November 14, 2013 at 9:12 pm

The lecture material and presentation are superb, but the graphics are hard to read/understand. But, still excellent coverage. -r.

• July 31, 2015 at 1:30 pm

The quality is not good but he explained very well…!!

• February 12, 2016 at 12:22 am

There is no gaps in Real numbers?

• February 13, 2016 at 1:58 am

What's the difference between math analysis and calculus? Why there is such distintion?

• May 12, 2016 at 9:43 pm

Hi NPTEL, the video resources u offer r at least as good, if not better than MIT OCW. However, I do think it's a shame that there is a significant number of lecture series (including this 1) that r at such low resolution that I cannot read the lecturer's notes! is there any chance that u will b refilming those series with higher resolution?!

• May 24, 2016 at 6:25 pm

Great.

• May 26, 2016 at 5:55 am

Does he mention which textbook he's using?

• July 18, 2016 at 4:02 am

only one lowpoint low resolution please try to reflm them

• August 10, 2016 at 12:08 pm

all here can't read notes can on subtitles

• August 31, 2016 at 6:25 am

please sir visible clearly is not seen in online lecture .so,keep neccessory steps towards it.

• September 29, 2016 at 5:24 pm

i want at least 480 p resoltution

• December 27, 2016 at 8:07 am

TYPOS AT 8:33 AND 54:12

• January 23, 2017 at 8:37 pm

what u write isnot visible sir ,

• June 11, 2017 at 5:25 pm

sir is that video and other related of this course is also useful for graduation?

• October 3, 2017 at 5:25 pm

The beauty of mathematics,……….in 240p( starts crying).

• January 9, 2018 at 7:05 pm

1/2 is between 1 and 2 amazing iit teacher

• January 22, 2018 at 1:02 pm

Not running on 360p&480p

• February 9, 2018 at 9:18 pm

Thank You so much sir !! 🤗

• March 13, 2018 at 2:57 pm

From..41:47 video is not working please fix it..I need this teacher so badly

• June 1, 2018 at 9:24 pm

got lost in 30 sec. back a few dozen steps now..

• June 24, 2018 at 5:17 pm

At 54:10 he made a mistake he said epsilon <1/n instead of epsilon>1/n

• December 19, 2018 at 2:29 pm

Can some one explain clearly what he means "Then I say that the proof is intuitively clear" at 14:22. How he says that r+(1/n) also belongs to the set A from the proof he gave

• December 29, 2018 at 11:37 am

If root 2 is irrational how can it has finite length in Pythagoras triangle…..

• May 28, 2019 at 11:46 am

bogus video quality

• May 31, 2019 at 6:27 am

Video gets stuck at 41 min

• July 13, 2019 at 6:54 am

Explanation is nice but video is worse