"Limit" is the basic concept of calculus, a branch of mathematics. The "limit" in a broad sense is "infinitely close and never reached". In mathematics, "limit" means that a variable in a function gradually approaches a certain value A in the process of getting bigger (or smaller), and "it can never coincide with A" ("it can never be equal to A, but taking a value equal to A' is enough to obtain a high-precision calculation result), and the change of this variable is artificially defined as" forever approaching ". Limit is a description of "changing state". The value a that this variable always approaches is called the "limit value" (of course, it can also be expressed by other symbols).

In mathematics, continuity is an attribute of a function. Intuitively, a continuous function is a function in which the change of the input value is small enough and the change of the output is small enough. If a small change in the input value will cause a sudden jump, or even the output value is uncertain, the function is called a discontinuous function (or discontinuous function).

The most basic definition of continuity is the definition in topology, which will be discussed in detail in the term continuity function (topology). In order theory, especially in field theory, another abstract continuity is derived from this basic concept: Scott continuity.