Ready SET Go!!!

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by dotsandlines

by dotsandlines

We use the words crowd, team, group or gang (not seriously) quite often. In mathematics, all such collections are called SETS. ( Capital letters have been used for emphasis, but you can scream them inside your head.) So, a set is simply a collection of objects. These objects may not necessarily be numbers.

Like for example you can make a set of anything you want. Just imagine them together inside your head. And we humans quite often do so. Like when you plan to pack your school bag, you form a set of subjects for the day inside your head. Or when you go through a menu at a restaurant, you make a set of all the food you could possibly stuff in your stomach.

We can write a set on a paper too. Just write down all the objects of your set , separated by commas and enclosed in braces. Let me give you an example, the following is the set of ingredients you need to make peanut butter and jelly sandwich:

{peanut butter, jelly, bread}

That's it! And when you thought it couldn't get any better, you can name them too. And that too anything you want. I am going to name my set I AM VERY HUNGRY. Why? Because I want to. So I write,

I AM VERY HUNGRY = {peanut butter, jelly, bread}

But its not always convenient to have such big names. So I can simply call it H.

H = {peanut butter, jelly, bread}

Lets bring in some numbers, shall we? We use the numbers 1, 2, 3, 4..... and so on , extensively in daily life. A set of these numbers would look like this:

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

( I read this as N equals 1 comma 2 comma 3 comma 4 comma dot dot dot dot dot dot. Which actually means that the sequence of number never ends! Trust me or try to tell the last number!)

There is a reason why I called this set N, because the numbers 1, 2, 3,..... are called NATURAL NUMBERS. But we will keep that aside for the time being.

A useful idea is to imagine sets as boxes containing objects. The box named H contains peanut butter, jelly and bread. The set N contains the numbers 1, 2, 3,......... . (So many numbers? That must be a berry berry big box!)

The following is the set of all the delicacies I can cook. I will name the set F.

F = { }

Well, I did not forget to put something in the set, I just can't cook anything. And YES! a set can be completely empty. Imagine it as an empty box.

You may be well familiar with the next set:

1D = { Harry, Louis, Liam, Niall}

( No I am not a fan. Its just the only band I know the names of all the members of.)

Imagine a box containing Harry, Louis,.......uh no don't! Now since Harry is in 1D, we say that Harry belongs to 1D. Similarly Louis, Naill and Liam also belong to 1D. While Zayn does not belong to 1D. Likewise, peanut butter belongs to set H , 1 belongs to set N. Ketchup does not belong to set H and the word Freeshevacadoo is not in the set N, so we say Freeshevacadoo does not belong to N.

But using the words belongs to always is sometimes tedious, use a lot of ink and paper, so we use the following symbol: ∈. Thus , Harry ∈ 1D ( read as Harry belongs to 1D ). Peanut butter ∈ H and 3 ∈ N. And when something does not belong to a set we use: ∉. Thus , Zayn ∉ 1D , Ketchup ∉ H and Freeshevacadoo ∉ N.

So....... That's all the set theory I have for today. Hope you learned something. Mathematics originated from the human mind, so it can be learned with the help of intuition. And anybody can learn maths! So stay positive and eat pi(e)! The universe loves you! Bayeeeeeeee!!!!