Infinity is a thrilling mathematical representation of something that our human mind can hardly imagine. When we think of infinity, we should think that:
- It is not big;
- It is not even huge;
- It is neither something tremendously large;
- Nor is it something enormous;
- It is just endless!
Yes, infinity has no end. In our world, we have nothing like this, and this is why we cannot imagine it, although many of us accept it. Because it is endless, infinity can never grow. In fact, it does not have to do anything, but just be.
What Is Then Infinity?
Some might think that infinity is a number, a real number perhaps. It is no such thing, it is just an idea, an idea about something that does not have an end. There is no way to measure infinity. Those who say that faraway galaxies would be infinite are wrong, because a galaxy always has limits, while infinity does not, and nothing can compete with it. Unlike finite things that surround us, infinity is simple. Just because it has no limits, we do not have to define it, while finite things have to be defined as size, weight, form, color, and so on.
To illustrate this, think of simple geometric representations of a line. According to its definition, a line has infinite length in both directions. A line segment, instead, has a length and we have to mention it. To take another example, the row of natural numbers is infinite. We count: 1, 2, 3, and could never stop, because no number is the last in this row.
However, we can have the same thing represented in two different manners. Let us consider a fraction like 1/3. This is certainly a finite number – the third part of a whole. But what happens when we write it as a decimal number? We should write 0.3333333…, with an infinite number of 3s, but this is not possible, because we could never stop. This is why we say “0.3 repeating” and write it like this: 0.(3).
Man has always tried to reach infinity, hoping that there was a limit to it. This is how huge numbers appeared, like a “googol”, which can be written as a 1 followed by 100 zeroes, or a “googolplex”, which is a 1 followed by a googol of zeroes. However, these numbers are also finite, no matter how much time it would take to write them down.
In the meantime, infinity keeps being an idea of something that never ends.