Final answer:
A sequence (xₙ) converges to a limit number L if for any positive number ε, there exists a positive integer N such that for all n greater than or equal to N, the distance between xₙ and L is less than ε.
Step-by-step explanation:
In mathematics, a sequence (xₙ) is said to converge to a limit number L if and only if, for any positive number ε, there exists a positive integer N such that for all n greater than or equal to N, the distance between the n-th term xₙ and the limit number L is less than ε. In this case, the sequence (xₙ) converges to L.
For example, let's say we have the sequence (1/n). As n gets larger and larger, the terms of the sequence get closer and closer to 0. Therefore, we can say that the sequence (1/n) converges to 0.
It's important to note that not all sequences converge. Some sequences may diverge, meaning they do not have a limit.