We can say that it matters in the sense that it allows you to compare the segment from 0 to 1 with the set of all real numbers and conclude that they are of equal power. Indeed, it is quite easy to establish a one-to-one correspondence between them, for example, like this: y = log ((1 - x) / x), where x is a number from the interval (0, 1), and y is any real number. If you want to include the boundaries of the interval, you can expand the corresponding set of real numbers with infinities.
Here's a fun fact - one set is a subset of another, and they have the same cardinality. The same trick can be performed with a set of natural numbers, removing from there, for example, all even ones.
This is another achievement of science. It can be the pride of the scientific world, proving the limitless possibilities of scientific thought. This is a fundamental knowledge that every person who respects science should know.
And so nothing.