There are uncountably infinite Irrational Numbers and their existence has been known for over 2500 years. In some cases, although their irrationality was suspected, rigorous mathematical proof took longer. Some notable events:
sqrt(2): Pythagoreans (6th Century BCE).
pi: Johann Heinrich Lambert (18th Century).
e: Leonhard Euler (18th Century).
In the late 19th Century, Georg Cantor proved that the number of irrationals is an order of infinity greater than the number of rationals.
The history of irrational numbers is quite simple in that any number that can't be expressed as a fraction is an irrational number as for example the value of pi as used in the square area of a circle.
Irrational numbers are real numbers.
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
There are an infinite number of irrational numbers.
The history of irrational numbers is quite simple in that any number that can't be expressed as a fraction is an irrational number as for example the value of pi as used in the square area of a circle.
They are irrational numbers!
They are numbers that are infinite
Irrational numbers are real numbers.
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
properties of irrational numbers
No. Irrational numbers are real numbers, therefore it is not imaginary.
Yes, no irrational numbers are whole numbers.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
No, but the majority of real numbers are irrational. The set of real numbers is made up from the disjoint subsets of rational numbers and irrational numbers.
There are an infinite number of irrational numbers.
All irrational numbers are not rational.