How large is Infinity?

A very common question that rises with the word Infinity is How large is Infinity. Imagine there are infinite number of pens and are distributed to infinite number of people one by one in a queue. The cycle of giving pen to the people will never end even if people grow old and time pass, it will still continue. So far, the discussion concerned about the smallest type of Infinity (countable infinity), like the set of Natural numbers. If there is a set of infinite cakes and each cake can still be assigned to a natural number and people would never run out of natural numbers. Thus, a set of Natural numbers is a countably infinite set. 

But one can have infinitely bigger set that contains all the numbers between two natural numbers, and this will be a bigger set than a set of natural numbers. Here, there are a group of numbers in between 2 and 3 which will be in decimals and the will never end (tends to infinity).

Thus we can not determine the extent of infinity. Infinity is undefined and we can not measure it. We can only imagine it.

There can always have another bigger set that is not in one-to-one correspondence to the original set by just finding the collection of all the subsets of the initial set. This will be an infinite tower of infinity which leads to something called Absolute Infinity. One can only have a sense of what infinity is and its way more bigger than one could ever imagine.

In simple words, what’s beyond infinity?… is infinity again and so on.

Also, Check

• Facts about Infinity
• Is infinity a Number

Infinity is a bigger than any number you can imagine but we can not determine exactly how much bigger is infinity. The simpler part about the word “Infinity” is that it does not have an end, and since, there is no end defined for the word, the end is not required to be defined. The word Infinity is represented by the symbol ∞ which does not belong to any Integer, real number, fraction, etc. When “infinity” comes in picture, what number pops up into the head? 

• Billion – 10⁹
• Quadrillion? – 10¹⁵
• Googol? – 10¹⁰⁰
• Googolplex? –  10^Googol

But is this infinity? NO.

Let’s understand how big is infinity in this article. Before learning, let us first go through the concept of number line.