Changes and permanents in mathematics

Changes and permanents in mathematics

Some people have some fear about algebra that they do not even know themselves. Algebra is the most compact forms of mathematics. It also gives the generalized forms of mathematical rules.

For those who are used to looking at numbers, seeing x and y can be intimidating. That threat is unnecessary.

Some of us have a habit of calling every puppy we see by the name Johnny. There is a habit of calling all the kittens by the name Nimmi. According to them Puppies are Johnny and kittens are Nimmy.

Now let us raise a question. Is he calling a puppy? Johnny? What is this question? As far as he is concerned, you will answer that Johnny is the puppy and Johnny is the puppy. Similarly Nimmi is a kitten for him, isn't Nimmi a kitten?

But how many types of puppies are there? Take particular note of the colors. There are many colored puppies like black puppy, white puppy, gray puppy and red puppy. But what will he call the puppy when he sees it? He calls himself Johnny. You can understand the algebra by naming in what he calls Johnny like this.

Needless to say, there are a lot of numbers in the Mathematics. Saying each number means you can continue saying it for the rest of your life. Now let's take natural numbers. 1, 2, 3, 4, 5, …. For all these numbers, it would be convenient to name any puppy like Johnny. These numbers are called n. You're right if you think they're calling you like a pet name Johnny. Now what is n? That is 1, 2, 3, 4, 5, … some number in this, Yes, you are correct. So, please, don't get mad at me for not even knowing this.

Similarly unknown numbers i.e. all numbers to be found are called x. What do you understand now?

Do you think that you will say only the puppy in detail and leave the kitten in detail? Bharathiyar himself has sung about it. Why are we saying here? Isn't he the poet who said that the mathematics as bitter, difficult and unfruitful? At the same time, wasn't he the one who sang the mathematical number that India's population was thirty crores at that time?

You must have read Bharatiyar's song "A white cat grew up in our house". Bharatiyar sang that the cat gave birth to many colored kittens. In that song, he has written about kittens of various colors like a milk white kitten, a gray kitten and a snake colored kitten. Now if we were to name the kittens algebraically, we would have to name them Nimmi. That's how numbers are named with English letters. Those letters represent all the numbers as we define them. That is, if x is a rational number then it represents all rational numbers. If x is a natural number then it represents only natural numbers. The ratio ½ does not represent a number as x. Have you any confusion?

If we come to the story of the puppy and the kitten, we will understand. Does Johnny mean kitten? It doesn't mean. Does nimmi mean puppy? It's not meant to be. Because we call the puppy Johnny. We call the kitten Nimmi. So that's how we define it.

Let's call the puppy as Nimmy and let's call the kitten as Johnny, we need to define that first. That means you have to tell the pet name while opening the mathematics. If you say that, you can keep the puppies as Nimmi and the kittens as Johnny. Do you understand now?

So you are saying that these x and y values ​​are not permanent and can be changed at will. That's right. You have reached the right place. These pet names are not permanent. It is to keep ourselves. It's about defining mathematics as far as relevance is concerned. What I consider x, you may consider y, another may consider z. That's why they are called variables in mathematics. So let us tell you how we define these variables.

If you tell the same puppy story again, you will understand clearly. One can pet the puppy as Johnny. Another may call it a chutty. Someone else might call it a kutty. How do you call it? If I say that's what I'll call the puppy, that's it.

A puppy is permanent. Names may change. Similarly numbers are permanent. The names of the variables held for it can be changed. The values ​​assigned to it can also change. Since numbers are permanent ant we call them constant in the sense that they do not change. We call variables x, y, z because their names and values ​​can change.

All letters a, b, c, … up to z are variables.

Not only numbers starting with 1, 2, 3, … but all types of numbers are constants.

A set with these variables and constants are algebraic expressions. Algebraic equations if set of expressions have equal symbol.

You may ask, what do you mean you are suddenly saying out new words like expressions and equations?

Expressions are just a mathematical arrangement.

For example you add two numbers. 2 + 3. It is an expression. If we say the same with variables x + y.

Equations are equating expressions on both sides of an equal to symbol.

Does adding two and three give 2 + 3 = 5? It is an equation.

If we say the same using variable x + y = 5. This is an equation. If we come to an equation and both sides of equal to symbol are equal, then it is an equation. That's it.

I understand what you're asking yesterday when you told us we were going to look at the formulas for perimeter and area and then you're talking about variables and constants like this. I think I have taken up too much of your time and gone into too much detail as these are fundamental to understanding the algebraic forms of formulas. So tomorrow we will move on to formulas.

*****