"More reals than rationals" is a statement in mathematics that refers to the fact that the set of real numbers is larger than the set of rational numbers. In other words, there are infinitely more real numbers than there are rational numbers.
One way to prove that there are more reals than rationals is by using a technique called "Cantor's diagonal argument." This involves constructing a real number that is not in the set of rational numbers, thus showing that the set of real numbers is larger than the set of rational numbers.
The concept of "more reals than rationals" is important in mathematics because it helps us understand the infinite nature of the real numbers. It also has practical applications in fields such as computer science and statistics.
Yes, one example of a real number that is not a rational number is pi (π). Pi is an irrational number, which means it cannot be expressed as a ratio of two integers. Other examples of irrational numbers include the square root of 2 (√2) and the golden ratio (φ).
Yes, there are sets of numbers that are larger than the set of real numbers. For example, the set of complex numbers is larger than the set of real numbers. This is because the set of complex numbers includes both real and imaginary numbers, making it an even larger set than the set of real numbers.