The symbol of vertical line is the representation of limit in differential equation. "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" refers to a variable in a function, which gradually approaches a certain value A in the process of permanent change (or source decreasing) and "can never coincide with A".

The origin of limit

The germination of limit thought can be traced back to ancient Greece and China during the Warring States Period, but the concept of limit first appeared in arithmetica infinitorum by Wallis, and Newton explicitly used the word limit in Mathematical Principles of Natural Philosophy.

But as late as the second half of18th century, D'Alembert and others realized that calculus would be perfect if it was based on the concept of limit. Cauchy first gave a descriptive definition of limit, and then Verdot Strass gave a strict definition of limit (ε-δ and ε-N definitions).