Infinities larger than others

 Hei Inspektører

Speaking of mathematics, can we say that there are infinities larger than others?

Lately I have been delving into these issues that, although they have a direct applicability in the engineering area where we develop as inspectors, I also believe that they are adapted to practically any daily concept.

For example, I was reading a while ago about a mathematician named Georg Cantor who in the 20th century showed that not all infinities are equal. (speaking clearly, of numbers, excluding a certain well-known eponymous business in my hometown)

What was Georg Cantor's explanation? Simple. He first wanted to match odd and even numbers by discovering that both sets of numbers are infinitely equal.

Then he wanted to match rational numbers with whole numbers and here he noticed that there are more rational numbers than whole numbers, since there are infinitely many decimals between 1 and 2 for example. (That is, the number of decimal numbers is directly more infinite than whole numbers)

The idea in general was rejected at the time by other scientists contemporary to Cantor such as Kronecker who believed more that this topic belonged to the field of philosophy or the Swede Gösta Mittag-Leffler who questioned Cantor's reputation in the field of the maths.

So, we have more than one infinity (finding infinity then infinities) and we also deduce that there does not exist as such a set of numbers (infinities) that is greater, there will always be a greater one.

As far as I read, this statement is true but cannot be proven.