Introduction to Real sequences; convergent, divergent and oscillating real sequences
First, let's try to understand what sequences really are. So formally, " A sequence in a non-empty set A is a function from ℕ into A. " In particular, a real sequence 'a' is a function from ℕ into ℝ . i.e., a: ℕ → ℝ . The n th term of the sequence is denoted by a n . Since a sequence is fully described by describing a n for each n ∈ ℕ , some of the ways in which we denote a sequence are: VISUAL REPRESENTATION Imagine a red dot flashing, first at a 1 , then a 2 and a 3 and so on. The dots keep on moving until it disappears, i.e., it moves towards infinity for the sequence of natural numbers. So, the orde...