Question

英文翻译，急用！！！

then the function f(x) is said to be continuous at X。 ; otherwise, f(x) is said to be discontinuous at X。 .
The abave definition can also be expressed in “ ”mathematical language as follows:
,such that |f(x)-f( )< for all x satisfying |x- |< .
It should be noted that unlike in the definition of limit ,for the definition of continuity , it is not necessary to require | x- |>0, because the definition requires f(x) to be defined as f( ) at x= .
Similarly , we can define left-sided continuity and right-sided continuity by the following one-sided limit respectively:
It is easy to prove that the necessary and sufficient condition for the continuity of f(x) at is that at x= f(x) is continuous from the left and also from the right .at That is
If f(x) is continuous at every point of an open interval (a,b) then f(x) is said to be continuous in the interval (a,b); if f(x) is continuous in the open interval (a,b) and is continuous from the right at the left end point of the interval x=a and is also continuous from the left at the right end point of the interval x=b , then f(x) is said to be continuous on the closed interval [a,b];if f(x) is continuous in an interval I, then it is called a continuous function in this interval I ; if I is just the domain of definition of this function then f(x) is called a continuous function . The graph of a continuous function is a continuous curve.
Henceforth ,we use the symbol C(I) to express the set of all the continuous function in the interval I ,that is ,
C(I)={f | f is continuous in I }.

Answer 1

然后功能 f(x) 被说对 X 是连续的。 ; 以别的方式， f(x) 被说对 X 是不连续的。
abave 定义也可能被表达在 "" 数学的语言依下列各项:
,以致于 |f(x)-f()<为所有的 x 满意的 |x- |<.
它应该被记录那不像在界限的定义中，为连续性的定义，它对需要 |x 不是必需的- |>0,因为定义需要 f(x) 在 x 被定义为 f()=.
同样地，我们能定义下列各项的左边- 边的连续性和右边- 边的连续性一-分别地袒护界限:
它是容易的必需品和充份的情况为 f(x) 的连续性在是在 x=f(x) 从左边是连续的以及从右边。在那是如果 f(x) 然后在一个开着的间隔 (a,b) 的每点是连续的 f(x) 被说是连续的在间隔 (a,b) 中;如果 f(x) 是连续的在开着的间隔 (a,b) 中并且在间隔 x 的左边结束点从右边是连续的= 一而且也在 interval x= b 的右边结束点从左边是连续的 , 然后 f(x) 被说是连续的在关闭间隔上 [a,b];如果 f(x) 是连续的在一个第一间隔中, 那么它被收回一个连续的功能第一这一个间隔；如果我只是这一个功能的定义领域那么 f(x) 叫做一个连续的功能。 连续的功能曲线图是一个连续的曲线。
自此以后，我们使用符号 C(我) 表达第一间隔的所有连续的功能组合 , 也就是说 ,C(我)={ f| f 是连续的在我里面 }.