A transcendental number is a number that is not the root of any integer and it is an irrational number. In other words, No rational number is transcendental and all real transcendental numbers are irrational. There can be uncountable transcendental numbers. Some examples are given here:

\(\pi ,\;e,\;4\pi ,\;\frac{\pi }{2}\) etc.

The numbers of the form of \(a^b\) where \(a\) is not 0 or 1 and \(b\) is an irrational number are also transcendental numbers. For example \({3^{\sqrt 2 }},\;{2^{\sqrt 2 }}\) etc .

Note that sum or difference of two transcendental numbers can be a rational number. For example \((\pi  - 1)\) and \((4 - \pi )\) are both transcendental numbers, but sum of these numbers  \(\pi  - 1 + 4 - \pi  = 3\), is a rational number. Similarly \((4 + \pi ) - (1 + \pi )\) is also a rational number.