How Big is Infinity?

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.

Number Line is a line on which numbers are placed at equidistant from each other. As a straight liner never ends, the number line too never ends. One can always think of the biggest number one could imagine, but adding 1 to it will make the number bigger. Thus it goes on and on.

So, the length of line will go every time we put a next number on the number line and this process will never end. So there are undefined numbers and undefined length of the line. This is what infinity represents.

Few examples of Infinity:

• 1/3 = 0.33333…..
• ⨅ (pie) = 3.1415926….
• Infinity + Infinity = 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

What is infinity?

Infinity is a concept that describes something without any limit. In mathematics, it is often used to represent an unbounded quantity that is larger than any finite number.

Can infinity be considered a number?

No, infinity is not a number in the traditional sense. It is a concept or idea used to describe quantities that are unbounded or limitless. It does not behave like finite numbers in arithmetic operations.

Are there different sizes of infinity?

Yes, there are different sizes or levels of infinity. This concept was introduced by mathematician Georg Cantor.

What is countable infinity?

A set is countably infinite if its elements can be put into one-to-one correspondence with the natural numbers. This means that even though the set is infinite, its elements can be listed in a sequence

What is uncountable infinity?

A set is uncountably infinite if its elements cannot be listed in a sequence that corresponds one-to-one with the natural numbers. The real numbers between 0 and 1, for example, form an uncountable infinity because there are more real numbers in any interval than there are natural numbers