The definition of convergence is as follows:

1. Convergence is an economic and mathematical term that is an important tool in the study of functions that converge on a point, moving closer to a certain value. Types of convergence are convergent series, function convergence, global convergence, local convergence.

2. Convergence is a Chinese word, pronounced shōu liǎn, which means to harvest crops; to collect rent; to gather; to collect; to summarize; to check one's behavior, to restrain the body and mind; to stop; to disappear. From "Zhuangzi - Let the King".

Properties of convergence of a function:

1. Convergence at x0, there must exist a decentered domain of x0 in which the function is bounded.

2. Convergence at x tends to infinity, in positive infinity, for example, then there must exist M such that the function is bounded on [M,+∞).

In general, continuous functions are bounded on closed intervals. For example: y=x+6 has a minimum value of 7 and a maximum value of 8 on [1, 2], so it is said to be bounded as its function value varies between 7 and 8, so it has boundedness. But the tangent function is unbounded in meaningful intervals such as (-π/2, π/2).