Between any two real numbers say 0 and 1, there are infinitely many rational numbers and infinitely many irrational numbers. Do you know that number of rational numbers is countable infinity and that number of irrational numbers between the same two numbers is uncountable infinity?
Is it sounds absurd?
Let us see why numbers of irrational numbers are uncountable infinite and are way more than a number of rational numbers between the same two rational numbers.
We know that a rational number in its decimal form is repetitive or terminates for eg. 0.432000 or 0.54545454..... On the other hand, irrational numbers in their decimal form are neither repetitive nor terminative for example 0.1213141516....
Lets us now create a number randomly,
Every time we place a digit we have 10 options of digits. How likely is it probable to get repetitive digits or 0 after a certain number? Of course very unlikely and at least very-very unlikely as compared to non-repeating ones.
These non-repeating ones are irrational numbers, thus the number of irrational numbers will be much more than the number of rational numbers between any two real numbers.
Hope you enjoyed learning a new Math Idea.
Happy Intuitive Learning.