Definition: for every given arbitrarily small positive integer ε, there is always a positive integer n, so that for n >；; Everything in n

x？ n？ , unequal? x? n？ -a︱<； ε can be established, so the constant a is called sequence X? ，X？ ，X？ ,。 . . ，X？ n？ ,。 . .

The limit of n→∞.

Your example is X? n？ = 1/n, which is proved by the limit definition: n→∞lim( 1/n)=0.

It is proved that the given positive number ε is so small, from ︱1/n-0 ︱ =1/n1/ε, so the positive integer N= 1/ε can be taken as

N> when n, there is always1/n.

What does this mean? That is to say, no matter how small the positive number ε you gave in advance, I can always find a positive integer n. From then on, that is to say,

Is n>n followed by x? n？ The values of = 1/n are all less than ε. For example, given ε=0. 1, there is n =10; When n >; 10, that is,11,112,

1/ 13, 。 . . . , all less than 0.1;

Given ε=0.0 1, there is n =100; When n >; 100, that is,11,1102,1103. . . . , all less than 0.0 1.

It should be noted here that this process cannot be repeated, that is, after n>n, at any time, the inequality ︱X? n？ -a︱<； ε has always been true, but it can't be true after a while!

How many heroes are stumped by the definition of limit! How many heroes have you charmed!