An ancient Greek mathematician in the era of Pythagoras is said
to have been murdered by his fellow secret society members for
discovering the (now well-known) proof that square root of 2 is
irrational.

It is believed that irrational numbers were known in ancient India but there was no formal proof of their existence as a separate class of numbers. The proof is sometimes attributed to the Greek philosopher, Hippasus (several centuries later, 5th Century BCE).

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.

They can be rational, irrational or complex numbers. They can be rational, irrational or complex numbers. They can be rational, irrational or complex numbers. They can be rational, irrational or complex numbers.

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.

Irrational numbers can't be expressed as fractions Irrational numbers are never ending decimal numbers The square root of 2 and the value of pi in a circle are examples of irrational numbers

Both irrational and rational are real. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.

Irrational numbers are infinitely dense so that there are infinitely many irrational numbers between any to numbers. In fact, there are more irrational numbers between any two numbers than there are rational numbers in total!

You can not add irrational numbers. You can round off irrational numbers and then add them but in the process of rounding off the numbers, you make them rational. Then the sum becomes rational.

No, the set of irrational numbers has a cardinality that is greater than that for rational numbers. In other words, the number of irrational numbers is of a greater order of infinity than rational numbers.