Part 2/5:
- Irrationality: All transcendental numbers are irrational, meaning they cannot be expressed as the quotient of two integers. An example of an irrational number is π (pi), which is approximately 3.14159... and continues infinitely without repeating.
However, it is important to note that not all irrational numbers are transcendental. For example, the square root of 2 is irrational yet can be expressed as a solution to the polynomial equation ( x^2 - 2 = 0 ). This shows that while all transcendental numbers are irrational, many irrational numbers do not fall under the category of transcendental numbers.