Theoretically, there are an infinite number of natural numbers and an infinite number of real numbers. But does that mean there as many natural numbers as there are real numbers?
+128485 The natural numbers form an infinite - but countable - set because we put can these numbers in a one-to-one correspondence .....1 is the first number, 2 is the second, and so on.
The set of real numbers is infinite - and uncountable - as the mathematician Georg Cantor proved.
In simplistic terms, between any two numbers on the number line, Cantor showed that there exists an uncountable set of real numbers.....no matter how close together these numbers might be.....thus...there are more "numbers" between 0 and 1 on the number line than there are integers on the number line....!!!
+128485 The natural numbers form an infinite - but countable - set because we put can these numbers in a one-to-one correspondence .....1 is the first number, 2 is the second, and so on.
The set of real numbers is infinite - and uncountable - as the mathematician Georg Cantor proved.
In simplistic terms, between any two numbers on the number line, Cantor showed that there exists an uncountable set of real numbers.....no matter how close together these numbers might be.....thus...there are more "numbers" between 0 and 1 on the number line than there are integers on the number line....!!!
