Infinity

I n f I n I t y

~Jay Mehta

Infinity is not the biggest number, but it is actually how many numbers there actually are.

Although, we have different types of infinities - smallest type of infinity being the countable infinity, like natural and whole numbers.

Uncountable infinities are like the real numbers as you cannot even literally count the numbers between 0 and 1 in a finite amount of time. In fact, you cannot even start counting.

In the first case, i.e. the countable infinity, the time to count the number of terms easy finite. It may be long enough then the years we are about to live or it might take so much time that universe ceases to exist. But the time is finite.

Whereas, in the second case the uncountable infinity. The numbers between zero and one are so many that it exceeds the total number of numbers on the number line of whole numbers.

Let’s see it like this:

Whole Numbers	Real Numbers Between Zero And One
1	0.5032187964318529
2	0.0265982958595562
3	0.1548289526482663
4	0.0005592559598656
5	0.9862448264633184
………	………..

So, if we consider the above table and arrange numbers in such a way that:

• If we take a random number between zero and one while at the end of the last whole number we can generate a new real number which would be in between zero and one by just taking the first number from the first real number (in this case it is 5).
• Then we take the second real number and write its second digit from decimal point (in this case it is 2).
• We keep on doing so and add one to each digit that we have collected and subtracted one from the digit if it is 9.

Following the above-mentioned procedure for the given table, we get the first 5 digits after the decimal point as – 0.63565….. The number so formed by this method would be a number that was not taken by us in the first place and yet we wouldn’t have a whole number that can be assigned to it.

True but counter-intuitive!!

#Fact: There is the same number of even numbers as there are odd numbers and they are the same amount with odd and even both combined.

Confused?

At first, it sounds to be false. We clearly know that there should be half the amount of even numbers as compared to both of them combined.

But this intuition is wrong!!

Why? – Because if we do a one on one correspondence in both the sets we will have the same amount of numbers as both of them are infinitely long.

#InifinityIsNotDefined.

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~Jay Mehta

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