NATURAL NUMBERS- meaning, examples, biggest natuaral number, infinity

Easy Math

Once, my friend asked me, ‘Why do you think Math is difficult for students? I said, ‘there are so many reasons for difficulties. he asked me, Which is major one?

I said ‘Teacher’

What? ‘Teacher’? My friend looked at me with confused mind. ‘Most of the students are struggling in academic Math, Why?

I said, ‘Academic Math Teacher’as a professor of zoology he had a completely different idea, but he was not convinced, he asked me with utmost patience,

How come a Teacher? A child is finding difficulty while understanding Math unlike biology why?

I replied with smile, A teacher who teaches math has not understood MATH or his inability/ability to make ‘Easy Math’ not understandable. Even after a long discussion, he was not convinced. He asked me ‘Why Teachers are like that? I replied,

‘Teachers are not taught,

they teach what all was taught to them .

‘Easy Math’ is not taught,

‘Easy Math’ is not written yet,

but few know how to make certain math concepts easy. But they won’t write because that is their livelihood. There is no organized material in math till yet for easy learning.

As a child, I hate MATH, as a student I hate all Math Teachers, But as a human being having minimum commonsense I realized Beauty of beautiful Mathematics. For me MATH is sweetest & shortest language .It is a universe of wonders It is Aesthetic....................... But it is EASY

My friend continued to ask me,

‘As a successful Math Teacher, how do you teach Math? Can you teach me with any example?

I said, ‘tell me any Math concept’. He said, ‘I don’t know, go ahead yourself

Number System

I said “I will show, there are two ways to teach number system”. First one is your Mathematics teacher style.

N = {1, 2, 3, 4, 5 …} (They write on board)

Number system starts with 1, 2, and 3. . . . . . . . And so on, it starts with 1, 2, 3, 4…... and continues, it is a set, and it consists so many numbers which are countable. It is a big set, symbolically it is represented by letter N.................

(Recapitulation)

Teacher : 1) What is the symbol used to represent Natural Number

Student : N

Teacher : Good , How many natural numbers are there between 3 and 10

Student : 8

Teacher : Wrong, you don’t know? Between 3 and 10 , 4, 5, 6....... like that

Student : 6

Teacher : Very Good ,Now next concept.

My style,

NUMBER SYSTEM

Friend, I am explaining to you, be a student. Do you know “classroom”?

Students will be sitting in-front of the writable board between them an Animal is

coming and going. “Yes”. Can you tell me? How many students will be in any given Classroom?

Yes, it may be 20 or 40 or 50 or 57or 32……….. so many chances.

Yes you are right.

Yes, we know, that there may be 10 students or 11 students or 12 students. In any case no ten and half students or eleven and half students(11½) students.

i.e. Number of students in a classroom is either 10 or 11 no 10 ½ or 11 ½ same way number of dogs on the street is either 5 or 6, no five and half(5 ½) Number of trees in a garden 20, 30, 32 but not 20 and half.

Friend, examples what I have given here is something naturally existing. Naturally existing,

Naturally existed organism/objects starts with at least one (1)

Am I right? He said ‘yes ‘

Take anything which is naturally existed, Number of puppies , if it is there , then minimum (at least ) it starts with 1 naturally, then it should be 2 , then 3 then 4 , and so on I want you to understand ‘Number System’

In this Number System ,I want to discuss “Naturally existing Number System “

i.e ‘Natural Number’ which are existed naturally it self. OR

Number which can be used to count the things which are naturally existed.

So it starts with minimum 1, 2, 3, 4,................... So ‘Natural numbers’ which is a big group, it consists of so many countable numbers

It is represented by N, Symbol N (N for Natural number)

N= {1, 2, 3, 4, 5, 6,....................}

So my questions is

a) Why is not a natural number?

b) Why 1.6 is not a natural number?

c) What is the smallest natural number?

d) How many Natural numbers are there in between 3 and 10?

e) Is zero natural number?

f) Which is the biggest natural number?

My last question is What is the biggest Natural number?

Do you think 99 or 100

or 420

or 9999

or 99999

or 9898989

or 999989989899999

No, no, wait

Which is the farthest object you have observed so for? A Tree, a Ship in the sea, cliff of a hill, a star in the sky which one? It depends upon your viewing ability, you may use telescope. Which telescope? You can see star, galaxy etc etc.....

Similarly just by placing one number is front of the given number a given number becomes bigger, by repeating it , we can make it still bigger .How big? Very big. But we don’t know what is tha

So it is impossible to write the biggest natural number , it is impossible to read, therefore itis not existed, So biggest natural number is very very........ Big

How big? We don’t know i.e. ‘infinity’ symbolically

What is infinity?

Mystery has its own mysteries, and there are gods above gods, we have ours and they have theirs, That is what is known as infinity. By �Jean Cocteau

Infinity is a symbol to represent something very big number, But it is not a number, it is a symbol, which is not defined . The biggest natural number is not existed. The biggest natural number is (infinity) But still discussion is on about infinity, types of infinity, infinity is number or not?

As our conversation continued, I was asked by my friend, ‘Do you think teachers are not teaching as you teach?’ I said, most of them not, he asked, Why are they not? I said , either they don’t know or they are not so passionate .

He asked, why do you think only Math teacher? Why not other subject teacher?

I replied, Math is a subject which is dealing with concepts which are not known, not seen, not existed physically, which is completely abstract The biggest challenge of a Math teacher is creating pictures in the mind of the student about something which is not existed

‘Yes, yes’, he exclaimed, and asked me, you said once that there are so many reasons responsible for Math being difficult subject What is next one?

I said ‘Defective learning teaching method’

‘Defective learning?’ What is that? He asked,

I asked him. Who can manage a car efficiently? He said, Owner cum driver or a mechanic

I said ‘Wrong’ How? A driver knows how to operate, mechanic knows how to replace different parts of the car . I said , The correct answer is ‘The designer of the car’ means one who knows internal design of the car, who knows functions of each parts of a car ,can manage each parts in a better way.

What do you mean? He asked,

Same way, one who knows internal structure of Math can teach Math in a Easy way . OR One should teach internal structure of Math, then only both Teacher and students can enjoy the process of Teaching – Learning. But he was not agreed, He replied, What is that? Math is having internal structure? Math ?

I am asked by, you yourself said that it is abstract, which is not existed and now you are telling it has internal structure. How come?

You ‘Biology’ people think that only living organism having internal structure but it is not so

I continued ,For example if I write 2 x 3 = 6 it is information, it is right , but If someone asked himself or others why it is 6 Why not 7? then one who answer should know its internal structure. He looked at me 2 X 3 = 6 has internal structure? I said ‘YES’

He asked me with curiosity What is that?

I said, it needs lot of explanation, it needs explanation about human evolution and tendency of this animal towards comfort. He was controlling his body temperature, and asked me, to understand 2X 3 = 6 you need Darwin’s evolution?

I said , nothing to do with Darwin ,but it needs human history of evolution.

10 x 4 = 40 why? Because it is taught by math teacher or given in the math table.

Have you ever questioned yourself that ,why it is 40 only? Why not it is 46? What multiplication is all about? What is its internal structure? How it is designed?