Question

Show that it is not possible to choose a uniform random number from the whole real line.(In other words, we cannot dene a probability on the real numbers that can be considereduniform.)

Answer 1

Answer and Step-by-step explanation:

The real line is the line whose points are real numbers. The symbol used for the entire line is R.                

A point is chosen on line as the origin. Points are right or positive, and points to the left are negative.

The main properties of real numbers are commutative, Associative, and Distributive. Real numbers are closed, have an identity element, additive inverse, multiplicative inverse, and zero product. When we choose a uniform random number, it should satisfy all these conditions of real numbers.

Choose a random number on the real line; for example, when we choose zero (0), it does not satisfy the multiplicative inverse.

Multiplicative inverse is a x 1/a = 1, but for 0, 1/0 it is undefined.

Hence it is not possible for a  random number from the whole real line.