key term - Infinitely Close

Definition

When we say something gets "infinitely close" to another thing, it means that it keeps approaching without ever reaching it. In calculus terms, this means choosing x-values for our table that continually get smaller (or larger) so they approach our desired target value.

Related terms

Converge:

In mathematics, when a sequence or series reaches an unchanging value as we progress through more terms, we say it converges.

Limit Notation: Limit notation is a way to express the behavior of a function as the input approaches a certain value. It uses symbols like lim(x→a) f(x) to represent this concept.

Epsilon-Delta Definition: The epsilon-delta definition is a rigorous method for proving limits in calculus. It states that for any arbitrarily small positive number (epsilon), there exists a corresponding positive number (delta) such that if the distance between x and some target value (a) is less than delta, then the difference between f(x) and the limit L is less than epsilon.