Limit means that infinity approaches a fixed value. In advanced mathematics, limit is an important concept: limit can be divided into sequence limit and function limit. Refers to the maximum. Zheng Yizhi's fog 1 1: "The Standing Committee has really become a' long tail' meeting, and Tang feels that his patience has really reached its limit."
Zuway's Rock Cutting Water: "I don't know what is the emotional limit of human amazement. I was really shocked. " Standard definition of sequence limit: for sequence {xn}, if there is a constant a, for any ε > 0, there is always a positive integer n, so when n >: | xn-a |.
Limit can be divided into sequence limit and function limit.
The first step in learning calculus is to understand the necessity of introducing "limit", because algebra is a familiar concept, but algebra can't handle the concept of "infinity". Therefore, in order to deal with the quantity representing infinity by algebra, the concept of "limit" is carefully constructed.
In the definition of "limit", we can know that this concept bypasses the trouble of dividing a number by 0 and introduces an arbitrary small number of processes.
That is to say, the divisor is not zero, so it makes sense. At the same time, the amount of this process can be arbitrarily small. As long as it is less than any small amount in the δ interval, we will say that its limit is this number-you can think it is opportunistic, but its practicality proves that this definition is relatively perfect and gives the possibility of correct inference. This concept is successful.