Lec 01 - Natural Numbers and Their Operations
ฝัง
- เผยแพร่เมื่อ 4 ก.พ. 2025
- Prof. Madhavan Mukund
Department of Computer Science,
Chennai Mathematical Institute.
Concepts covered: Natural numbers, arithmetic operations, number system.
Learning outcomes:
1. Identify and list natural numbers and integers.
2. Distinguish between notations like ℕ, ℤ.
3. Understand the operations multiplication and division in terms of addition and subtraction respectively.
4. Identify quotient, remainder, and mod (modulus).
5. Find factors and prime factorize natural numbers. IIT Madras welcomes you to the world’s first BSc Degree program in Programming and Data Science. This program was designed for students and working professionals from various educational backgrounds and different age groups to give them an opportunity to study from IIT Madras without having to write the JEE. Through our online programs, we help our learners to get access to a world-class curriculum in Data Science and Programming.
To know more about our Programs, please visit :
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What a genius professor! Look forward to falling in love with mathematics studying under him!!!!
How is it going on
I am left with complete awe, how Professor Madhavan handles Maths.Thank you Professor!
Too Good. This is so thoughtful. Usually seen our education system punishing students for selecting stream years ago and makes it a dead end. I appreciate this initiative by IIT Madras to create a course, irrespective of previous stream that the student studied in. All the more, the thoughtfulness behind this Maths is amazing.
I want to bs online course lecture language
1) English
2) English+Hindi (mixed)
Love Prof. Madhavan's way of explaining. Many thanks to him.
anyone here for sept ?
yes
Yes
@@SagarUpreti-zk6ys studying for Sept qualifier right?
@@aviirell yes sir
Anyone here from bio group?
Thank you very much sir for providing the first week lectures. It makes very easy to learn the nature of course. And obviously these lectures are from IIT so the quality of education here is top notch. Feeling blessed that we are getting that high quality content of education, Thank You very much IIT Madras.
Brother ab kya haal hai apke maths mai 😂😅
Mai bhi lunga is saal enroll please reply
00:01 INTRODUCTION
00:11 LECTURE STARTS HERE
00:30 NATURAL NUMBERS
03:00 NEGATIVE NUMBERS
03:36 INTEGERS
04:06 NUMBER LINE
04:27 MULTIPLICATION & EXPONENTIATION
05:56 SIGN RULE FOR MULTIPLICATION
08:07 DIVISION
What is your current qualification
@@slightb😂
is a professor of IIT
@@KotaeffectLmao what
@@slightb 1st year BA
Excellently explained professor! I'm a fan
According to Stanford's Encyclopedia of Philosophy, natural numbers are often defined as "the POSITIVE integers {1, 2, 3, ...}." Zero is neither POSITIVE nor NEGATIVE. It is considered a neutral number that serves as the dividing point between positive and negative numbers on the number line. According to the University of Oxford, zero is the midpoint separating positive and negative values, and it does not belong to either category (Smith School of Enterprise).
That's what I was thinking, 0 is not in natural number set
*Sir, I have a Doubt!*
At 19:15, You said, _"a divides b, if a mod b is zero"._
I think it should be, _"a divides b, if b mod a is zero"._
Yes u r correct
I also have doubt, but for sure it's mistake and and I am considering factor "a | b" if b mod a = 0.
at 19:15 a divides b if b mod a is 0. The reference is at 10:58 . Thank you.
Even I noticed
same I thought.
Thank you sir 💓💓
I specially came from there site to TH-cam to like the video. Couldn't imagine math would be so much interesting.
WoW Sir👍 Great
Sir..My understanding is that Collection of Natural Numbers with predecessor of 1 is known as whole number....
why 0 is include in natural no. 🤨
Because:
The classification of 0 as a natural number depends on the context and the definition being used. There are two common conventions:
1. **Mathematical Logic and Set Theory:** In this context, 0 is typically included in the set of natural numbers. The natural numbers are defined as the set \( \{0, 1, 2, 3, \ldots\} \). This inclusion of 0 is common in areas such as computer science and certain branches of mathematics.
2. **Traditional Arithmetic:** Here, the natural numbers are often defined as the set \( \{1, 2, 3, \ldots\} \), excluding 0. This definition is commonly used in elementary mathematics and in many educational contexts.
Both definitions are valid, but the choice depends on the specific mathematical context and the convention adopted.
@@yruxotic_ ohkkk thnx dude🙏
Why because 0 (zero) has naturally a valued numbers before Ramanujam said that
@@yruxotic_ According to Stanford's Encyclopedia of Philosophy, natural numbers are often defined as "the POSITIVE integers {1, 2, 3, ...}." Zero is neither POSITIVE nor NEGATIVE. It is considered a neutral number that serves as the dividing point between positive and negative numbers on the number line. According to the University of Oxford, zero is the midpoint separating positive and negative values, and it does not belong to either category (Smith School of Enterprise).
lec 1 done✅ AQ1: 1- 4.5/5✅
hi buddy has the week 2 content been released?
@@ShivaHariny yes bro
Amazing Session Sir ✨
Shere your experience regarding this course I want to join the same course
How it is in foundation level.😮
@@yashashwikundan I Haven't Join the course too...
I will join this year ...
The qualifier exam will conducted on 7 July ....
Then the foundation level will start. ...
About Zero being a natural number, if my memory serves me right, we were taught in school that Natural Numbers start with 1. Zero was not considered a part of the Natural number set. Numbers starting from zero and upwards... 0,1,2... were considered a part of the whole number set.
So is there an agreement now that includes zero in the list of natural numbers ?
Yes if zero is added it becomes a whole number
Yeah! Even I've learnt that '0' is not included in the set of Natural Numbers. Can anyone please clarify and enlighten all of us?
@@AadityaVermaCS- but in cs there is no concept of whole number and the natural nums include 0. You can say whole num and natural nums are unified in cs language
@@rishabhprakash007 But what about fact that we're studying the subject 'MATHEMATICS for Data Science': meaning primarily MATHEMATICS, being in applied in DATA SCIENCE. And as far as MATHS is concerned, NATURAL NUMBERS are the set of tools which humans use to count things naturally. And you just can't count something which is zero naturally. And as far as the argument of subtracting a natural number from itself resulting in a zero is concerned; we've crossed the domain of 'COUNTING'; and gone to 'OPERATIONS ON NATURALLY COUNTABLE THINGS'. Please reply if you find my argument valid.
@@abhigyandsa Well you probably answered my question more or less by using the word 'STANDARD DEFINITION'. If something is standard then that doesn't change anywhere, irrespective of the context in which it's being used. For example, the definition of one second of time is, 'the fixed numerical value of the caesium frequency ∆ν, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1'. Which is fixed everywhere and STANDARD (as you very rightly used it).
Then my very humble question is, how can the STANDARD DEFINITION of NATURAL NUMBERS with respect to different contexts change??
Please answer my question if you find my argument logical and reasonable!
If you include 0 in the set of natural numbers then what about Whole numbers sir??
Usually, when we say Natural Numbers we just mean Positive Integers. And the concept of Whole Numbers arises only when we don't add 0 to Natural Numbers. Read Embedded Systems Dictionary - 2003 (ISBN : 978-1-57820-120-4) for more information.
@@parthpurvesh1201 sir in whole numbers we include zero
But in natural numbers we don't.
So it's like: N= {1,2,3,4.....}
Sir we are taught in school that 0 is not included in natural numbers.
It is included in whole numbers
@@eternalphoenix6077 The professor in this lecture said that he will be using the term Natural Numbers for all positive integers including 0, and there is no concept of Whole Numbers for the sake of this course.
you can avoid including 0 in natural numbers, by quoting N with the subscript '0' as mentioned by the professor @ 2:05, hope it helps.
9:08 but they are 5 friends how u can distribute the 20 mangos 20÷5=4 only four frnds have mangos but remaining 1 frnd does not have mango?
Lol bro, 4 is not friends. Its mangoes distributed to 5 friends 😂
🤣🤣
Bro is. Confused for universe
19:01 shouldn't it be like "Quotient is the integer number of times that the 'Divisor' goes into the number"?
yes exactly!!
Sir if you have notes pdf(all lecture slides in a pdf) kindly mail me please....
@@tonywilfred007 yes I have
Week1 Math1 Done ✅️
5:43 sir if we use dot it will look like a float value.It is better to use when we have variable.
0 is not included in natural numbers,is this a correction?
Natural Numbers - en.wikipedia.org/wiki/Natural_number
L1.1 Done AQ1.1 Done (5/5) ☑
I think zero will not be included in natural number. And whole number contains zero in the begining.
Is this lectures are useful for september 2023 batch qualifier exam ???
Yes
Yes 😊
19:13 Sir, you said "a divides b if a mod b is 0".
i believe it should be 'b mod a' or else it will always be 0
are we supposed to do this whole playlist before october 10th?
I have the same doubt. The email provided the link as sample videos and it turned out to be a playlist!!
no
only upto week 4 content. they have uploaded more than 4 weeks content in some of the playlists
18:21 Summary of the video
bruh u writtin everything in ur notes ?? just askin..
Thala for a reason 😂😂
😂😂
If A and B are Integers, then is (A mod B) an Integer or a Natural number?
Both are possible but depends on the value
when are supposed to do our 1 st weeks assignment
Graded assignment is at the end of the week one module and you have to submit it before 12 june .
@@PradhumnChauhan-qr9kiwhy are we getting TH-cam vedios as our lectures and not any exclusive ones because I think everyone can see these vedios but we paid for this
And also I am having issues
1. In course registration it's showing not applicable
2. Not recieved and roll number or I'd card just got a separate email id and password
Please help if u have any knowledge about this
Okay so, @nalayakhu8523 it goes like this, you paid to register for the test or qualifier exam not for the videos. And 2nd you'll get everything after you pass qualifying exam and get admitted to the course.
@@devankgupta4529 ok thanks 👍🏼 I am able to see the content and assignments but in my registration it's showing that not applicable and they are telling to mail at email id with screenshot of the page
where can i find first graded assigment??
AQ1.1 COMPLETED 5/5.
at 02:03 what is the difference between natural numbers and whole numbers?
We have been taught that whole numbers is combination of 0 and natural numbers.
8:26 shouldn't there be 5 parts with 4 mangos in each as there are 5 friends and each gets 4. And not 4 friends who each get 5 as in the picture.
same doubt
They didn't notice maybe
The Quarter represents the number of rounds in which the division has taken place and as you see in each quarter 5 mangoes are there for each friend. I hope this clarifies your doubt.
Hi guys any update regarding the live sesions? I got none!
No bro
how old are u bro i wanna become friends
@@SCYKICYT for sure, 18 u
Sir what is whole number
A number which is whole, now whole sounds like hole which we can represent as a o or 0 some people also say this is zero but what actually whole is its not a hole but something which is complete. Now zero is not complete but 1,2,3,4 is ,that's why the set of natural numbers without zero are called whole numbers 🤗
in pure mathematics, we have natural numbers and whole numbers, but in statistical (data analytics) maths, we only have natural numbers
so in pure mathematics, natural no. - 1,2,3,4 and whole no. - 0,1,2,3,4
whereas in statistical maths, only natural number exists -0,1,2,3,4
sir then what is the difference between whole number and natural number
Pever 🔥
Can you use black screen please,in white screen it actually gives a lot of pain to head and eyes 😢
Did you get any notification about the live class??
No man, even im waiting, can you update when you can see
He cant do it bro the video was uploaded 3 years ago 😂
At 19:13
" a divides b if b mod a=0"
16:28 sir 39 is not a prime number
When did he say it's prime ?
sorry sir but you have left something very precious on how numbers were actually originated from BHARAT , and its very sad to see such things ignored in our system , i liked the way how you explained but it needs improvement ,
first of all from the book of princeton maths
"Our system for representing whole numbers goes back,
ultimately, to the mathematicians of the Indian subcontinent. Sometime before (probably well before) the fifth
century c.e., they created nine symbols to designate
the numbers from one to nine and used the position
of these symbols to indicate their actual value. So a 3
in the units position meant three, and a 3 in the tens
position meant three tens, i.e., thirty. This, of course, is
what we still do; the symbols themselves have changed,
but not the principle. At about the same time, a place
marker was developed to indicate an unoccupied space;
this eventually evolved into our zero.
Indian astronomy made extensive use of sines, which
are almost never whole numbers. To represent these,
a Babylonian-style sexagesimal system was used, with
each “sexagesimal unit” being represented using the
decimal system. So “thirty-three and a quarter” might
be represented as 33 15
, i.e., 33 units and 15 “minutes”
(sixtieths).
Decimal place-value numeration was passed on from
India to the Islamic world fairly early. In the ninth century c.e. in Baghdad, the recently established capital
of the caliphate, one finds al-khw¯arizm¯ı [VI.5] writing a treatise on numeration in the Indian style, “using
nine symbols.” Several centuries later, al-Khw¯arizm¯ı’s
treatise was translated into Latin. It was so popular
and influential in late-medieval Europe that decimal
numeration was often referred to as “algorism.”
It is worth noting that in al-Khw¯arizm¯ı’s writing zero
still had a special status: it was a place holder, not
a number. But once we have a symbol, and we start
doing arithmetic using these symbols, the distinction
quickly disappears. We have to know how to add and
multiply numbers by zero in order to multiply multidigit numbers. In this way, “nothing” slowly became a
number."
one of the oldest use of numbers is in yajurved , shukla yajurveda
and there are plenty of proofs in mahabharat of established number system in india, his book name Al-Khwarizmi wrote "Kitab al hisab al Hindi" also see this en.wikipedia.org/wiki/Principles_of_Hindu_Reckoning
this is just about numbers
although i liked the way you explained , its great to see this passion
Great and feeling proud 🙏🙏🙏
Is there any pdf file of this content.?
Baadme aayegi, site pe
This is for bca sir
which books to purchase for this course ?
no books needed just videos and assignments
@@aryangarg5912 there are books if needed
@@yeshwanthmuthyala3343 where bro
@@aryangarg0608 you can download books online
@@dheerajsaini285 searching by topics?
Anyone here for february 2025
Yess
Me
Yes
Hi
I have a confusion if any one could help it will be great on your part
So basically i am preparing for qualifier exam for may 2023 and are these lecture helpful or this is same syll which they are going to teach or i am just wasting the time ..
I am also preparing for may 2023 and yes this lectures are helpful for qualifier exam as I have talked to the seniors they told that everything will come from these lectures uptill 4 weeks
Oh! Thats really great to hear
I just wanted to know that from where are u actually doing prep .i mean the ques for practice and all ..
@@tannuji6498 I am following the main youtube channel for studying the topics and after completing the topics I will give mock test as I have question papers of qualifier exams
@@tannuji6498 are you going to pursue dual degree or you are only going to pursue this single bs data science degree ❓
Both of you are qualified for jee advance or not and when is qualifier as i am qualifief for ja so what should I do please guide
I really had another serious doubt... If we write 7*4, we say 7 times four, which is nothing but 4 is added 7 times, or sometimes we say 7 fours are 28 which means group of 4 when added 7 times gives us total of 28, so why do we say that 7*4 is groups f 7 added 4 times??
plz anyone reply to my doubt....ASAP
Bhai apne quilfy kar liya kya
Awesome!!!!!!!!!
sir please clarify "Natural Numbers"
number from 1 onwards.. anything less than 1 is not natural
in data science 0 is also considered as natural number
im confused abt that mod is it a mod b or b mod a ? some1 give an example with numbers
the sentence say "a divides b if b mod a = 0"...lets us take a=4 and b=20 so 4 divides 20 if 20 mod 4 = 0..
Interesting perspectives!
Attendance of 2024 students ✋✋
hey can u tell me if this is the syllabus of the foundation course or the qualifier exam?
@@FreakOut167 for qualifier week 1-4 contents and for foundation, when you pass the qualifier exam then its depends upon % ,if you get >70 then you can go with 4 course or if you got >=50 then you will have 3 course and if you got 40 then you can do it 2 course. Other details please refer IIT Madras Website
@@RJjhunjhunu18hi can u tell me That we should do a regular college along this course or just doing this course is enough
Done
wait a minute 0 is a natural no. , seriously my whole life was a lie..
No, he didn't say 0 is a natural according to general principles of mathematics taught at the school level. He clearly defined the set for computing purposes and has mentioned this while doing so.
@@orange9923 BUT THERE IS A QUESTION IN ACTIVITY ASSIGNMENT IN WHICH YOU HAVE TO CONSIDER 0 AS NATURAL NO. TO GET THE RIGHT ANSWER
@@kingrajput6202 Yeah of course. The definitions mentioned here must be adhered to from a computational perspective and not in a strictly mathematical format.
@@orange9923 Thank you for clarifying!
0 is not a natural number, sir.
natural numbers with 0 is just whole numbers at that point
Same confusion at that point
@9.00 the question has to be 4 friends. pls correct it.
If multiplication is repeated addition, then why -7 * -4 is +28?
On multiplying minus with another minus...u eventually get a plus sign...so the logic is same...u end up adding 7 four times...in the same way if it would had been 7*-4 then here minus *plus is minus...but u are still adding 7 four times...and u just put an extra minus sign in front of 28...thats all
Excellent question! This is exactly why mathematical intuition is very important in building excellent mathematical skills.
Suppose you run a restaurant and you know that you make $ 10 an hour. You run the restaurant for 10 hours a day and at the end of the day you make 10 * 10 = $ 100 dollars. It’s not possible to run your restaurant without any expenses. So, let’s assume your total expenditure per hour is $5 and for the day is 10 * -5 = - $50.
Now, there are many categories of expenditure which in total equates to $5 per hour, which includes labour, electricity, inventory etc. Let’s say labour charges are $3 per hour but, 1/3 of your labour force were absent on a given day. So, on that day your labour charges would be 3 - 1 = $2 per hour.
Therefore, you would save(or make) $10 on that day. Now coming to the multiplication part of it; because the labours lost 10 hours on their job, it will be recorded on their account as -10 * -1 = $10 and it will be added as an income on the owner’s account.
I hope that helps. :)
i think distribution of mango is in wrong way five lines which a circule a right
So, here's the doubt
: why are we considering 0 as a natural number here? also, even if we do so, it's failing the condition of providing a natural number if we divide natural numbers, because we get 0/0 form.
Shere your experience regarding this course I want to join the same course
How it is in foundation level.😮
Zero natural number me include 🤔😢
We want this course in hindi + English language please😢
good and need to upload the whole course
It is already uploaded check Iitm TH-cam channel
@ 19:14 I think the Professor meant to say a|b if b mod a = 0 and NOT a mod b.
Yup .....had the same question
is 0 a prime number
no, a prime number has 2 factors, so 0 and 1 are not prime numbers
January 2022 batch 👊🖐️
conceptual clarity is missing... it seems confused with Natural numbers properties ... pl check...
I think he was pretty clear, Can I suggest you to watch watch that part again. I have watched this video twice and some sections more than twice.
Natural no. To phir whole no. K sath same ho jaega agar 0 include kardenge 😐
NEEDS TO MAKE MORE SIMPLE
they also asked this in upsc interview 😅😅
Where , please send video link
@@Shrutiyadav_108 comments with link is being deleted. Just search what are numbers upsc interview. There are multiple shorts and even the full video.
super
done
Yah man don't know how i gonna clear the qualifier test😅 in CT and maths
Marvolous 😁
2:42 😊
anyone from may qualifiers???
Yep!
13:30
Hey can you plz tell that the content for qualifiers remain the same every year?
bhaiiiii kya soultion milegaa
7:38 unfortunately XD
Might be into 2D beings👀😂
he looks like ramanjunan 😅
Fr fr
Ah shit! Here we go again
With new confusing usage of terms and symbols
'Mod' is already in use as short for 'modulus'
Why this again? can't these Mathematicians come up with something new?
Sep 2021 batch 👊🖐️
Hey! How's it going?
@@Ara-lm3zg great, I watched the first four lecture of maths and it looks quite easy. I will study the rest of them now.
Hey.. Please do tell me how to access the activity questions for video lectures as well as the graded assignments.
@@aadityalakshmi1343 Once you 'sign in' in the website, you can see an option of 'My current courses'. Click on them and you can see all the videos , graded assignment and non-graded assignment there
Natural number set doesn't include 0 😟😟 it's confusing, since there is already a set for natural numbers including 0, i.e., the whole number set. Please don't include 0 in the natural number set 😟😟
oka mukkka artham kala chepputhu kottu bro
😂
Aytaadhi bro language Prblm Vala Konchem Kashtam Gani Topics anni easy ga Unnai..!
@@AbdulRehman-tg5nn 😅👍
What a boring lecture..they should learn how to teach by seeing pw team
Boring tha ye lecture
Will this lecture be helpful for Qualifier xam???
What kind of a question is this? This videos are made for the sole purpose of Qualifier.
done