Let a be a real number and let δ be a positive real number.

Then the set of all real numbers lying between a - δ and a + δ is called the neighbourhood of a of radius δ

and is denoted by N_δ (a).

So, N_δ (a) = (a - δ, a + δ) = {x.R | a - δ < x < a + δ}

The set N_δ (a) - {a} is called the deleted neighbourhood of a of radius δ.

The set (a - δ, a) is called the left neighbourhood of a and the set (a, a + δ) is called the right neighbourhood of a.