We like to count. We count coins in our pockets, our family’s cars, the area of the house and the dollars of the national debt.
But when arithmetic appeared in the human discourse, the realization began that the numbers were continuing. The sequence of whole numbers, starting with a unit, can grow indefinitely.
We have come to the concept of infinity.
According to our daily vocabulary, Infinite is now incalculable. Scientists have suggested that our universe may be infinitely large, otherwise existence could contain an infinite number of universes. In religion we talk about our souls who live forever (i.e. indefinitely) and that our God has infinite power. In mathematics we can remember what our teachers talked about lines with an infinite number of points.
So let’s think about infinity for a few minutes.
For example, we may think that the number of even and odd whole numbers is greater than the number of odd whole numbers. After all, for any odd whole number we have two whole numbers, if we consider both the odd and the even. Thus, the number of even and odd whole numbers should be more than the number of only the odd whole numbers.
However, infinity does not make much sense. There is no “number” of whole numbers. Entire numbers are endless, which means they can’t be counted. But you can associate an infinite number of things.
So let’s link the odd whole numbers to all the numbers. We connect one with one, three with two, five with three and so on. Can we go on and on comparing each whole to the odd whole number? We could. Thus, in terms of infinity, a set of odd whole numbers refers to the same type of infinity as the set of all whole numbers.
So, do we have a secret? Can we use this binding technique to show that all the endless sets of things are the same size? Yes maybe. For example, after a little work, we can show that a series of fractions, that is, a number of numbers in which one whole number is divided into another, has the same size as a number of whole numbers.
But when we get to real numbers, it’s not. Real numbers are numbers with decimal signs, such as 2348. Here we see that a set of actual numbers is larger than a set of wholes. Let’s pair. We associate it this way:
1 with 0.1
2 with 0.11
3 with 0.111
4 with 0.1111
5 with 0.111111
6 from 0.1111111
We see we’re in trouble. If we convert whole numbers into actual numbers, we will see that we will never deviate from the actual number of 0.1 and its extensions. Thus, we will never be able to associate 0.2 or 3.28 with a whole number, for example, because a sequence of 0.1 will keep whole numbers occupied forever.
So we have more than infinity, or at least the infinity of whole numbers. Although we can’t count the number of whole numbers or the number of actual numbers, we showed (unofficially, mathematicians strictly do it) that real numbers are larger than entire numbers.
Is it relevant? Could be. Is God a monotheistic religion infinite just as infinite whole numbers, or as infinite actual numbers? That’s an interesting question. And humanity must continue to ask itself such questions in search of truth.
David Mascone was educated in engineering and commerce. He is interested in science, philosophy and theology. In his spare time he is engaged in sports, tourism, science fiction and competitions in refereeing. Its intellectual purpose is to find consistency and synergy between the great masterpieces of human intelligence, including religion, science and art.