Introduce the concept of the definition of a limit. A sequence of values of a variable "v" approaches a limit "l" if, starting with a certain term, the absolute value of "v" minus "l" for that term is less than a given, extremely small positive number.
Proceed to explain that if "x (or, "the change of x") is the variable, and its rational values approach a limit 0, for example, record the function as "x 0 ("the change of x for limit 0"). Therefore, there always exists a difference between 0 and the terms of the sequence. That means that there is always a difference between 0 and terms of the sequence.
Deduce that the definition is informing us that if we picked any given number "a," graphed it between two horizontal lines, we would be able to determine some other number "b" that would permit us to add in two vertical lines to the graph at a - b and a + b.
Look at the definition of the limit in mathematical language, now the basic principles have been established. The limit of "f(x)" as "x" approaches "a" is "L" if and only if, given e > 0, there exists d > 0 such that 0 < |x - a| < d implies that |f(x) - L| < e.
Broaden understanding of limit definition by performing practice problems.