# There is an infinite number of numbers between 0 and 1. What does this mean for science?

## Countable & Uncountable Infinities

Last update: 2 answers

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## Answer 1

January, 2021We 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.

## Answer 2

January, 2021This 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.