Infinity. Known for its unique representation as a sideways 8, and the value that children use to attempt to win arguments. Infinity is the representation of all numbers and values, all that there are and all that there will ever be, forever. It’s as if one drew a number line that kept counting up, and that line never ended, ever. Even after one billion years and light years of paper, there’d still be more numbers left to write on that line. It would be impossible to write every single number on that line, because one can keep counting upwards and downwards forever. While it is hard to initially wrap your head around, it’s a concept that has become ingrained in our everyday culture, describing things as “infinite” just for the sake of hyperbole. But, why is it important, or is it even important to begin with? Time to delve into numbers, in what is hopefully more interesting than your average math class.
Infinity often has a rather grievous misconception in the way it is seen. Infinity isn’t actually a number, nor does it even have a value. Like mentioned previously, infinity is merely a concept, or a rule. Infinity doesn’t have a beginning or an end, either. Again, considering infinity as our theoretical number line, it would stretch forever in both directions. The middle of the line would always be changing as the line extended, and the starting point itself can’t even be considered the beginning. More bluntly, to place a beginning or end on infinity would require one to answer two questions. “Where do values begin?” and “Where do values end?” (As a pre-emptive response, zero is not the starting point.) Those questions are, in the end, totally unanswerable.
To make matters even blurrier, humans can barely even comprehend infinity. Humans can barely even actually make sense of numbers such as one million. It’s why people can more easily understand that 10 out of 100 people dying during a disaster, as opposed to 10,000 out of 100,000 dying. As the numbers get larger, humans have more and more difficulty actually picturing the value. Trying to put infinity into a scale that humans can understand is literally impossible, to boot. Infinity is every single value, after all.
A bit deeper into the value of infinity, many people can remember the schoolyard arguments that were solved with the phrase “infinity plus one,” or “infinity plus infinity.” Weird part is, infinity plus one or infinity plus infinity still end up equal to infinity. No matter how much you add, subtract, multiply, or divide infinity by, it will remain as infinity. It’s so large that it can’t really be changed.
Yet, there’s still more confusion to be had. There are some infinities that are greater than others. The easiest example to picture is if one were to count two separate infinities. “All whole numbers,” (-1, 0, 1,2,3,4,5, etc) as opposed to “all numbers between 0 and 1.” An example of all numbers between 0 and 1 can’t even accurately be given, as there’s no way to know where to start. If you were to draw a decimal point, and begin writing zeroes, at what point do you stop and write a one at the end? The answer: never. The amount of numbers between 0 and 1 is so unbearably great that it cannot even be counted. That’s the easiest way to picture “Countable Infinities” and “Uncountable Infinities.” The existence of two separate infinities seems to contradict the previous few points of this article, and that’s what makes it so confusing.
However, what actually is infinite? It’s fine to talk about hypothetical values and how high or low they can go, but what can be called an example of infinity? There are very, VERY, few things that are tangible and infinite, with the most apparent being the universe itself. Looking up at the stars at night, some people would say that the blackness in the sky goes on forever. They’d be right. The universe that we all inhabit is expanding every instant, growing infinitely bigger at an infinitely faster rate. Meaning, the space we inhabit and the time we have is so unbelievably small compared to the scale of the universe that no one can even write how miniscule we are. There are always infinitely more things happening every instant, more than we could ever dream to comprehend. On a cosmic scale, our existence versus the universe is an uncountable infinity. Some may find it interesting, some may find it frightening to think about, but infinity is a concept that defines the universe we live in, so it can’t be ignored.