Difference between revisions of "Continuous"
(New page: A property of a function. Definition. A function <math>f: I\to\mathbb R</math>, where <math>I</math> is a real interval, is continuous in the point <math>a\in I</math>, if fo...) |
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A function is said to be continuous on an interval if it is continuous in each of the interval's points. | A function is said to be continuous on an interval if it is continuous in each of the interval's points. | ||
| − | An alternative definition using [[limits]] is <math>\lim_{x\to a} f(x) = f(a)</math>. | + | An alternative definition using [[Limit|limits]] is <math>\lim_{x\to a} f(x) = f(a)</math>. |
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Latest revision as of 11:52, 15 May 2022
A property of a function.
Definition. A function 
, where 
is a real interval, is continuous in the point 
, if for any 
there exists a number 
(depending on 
) such that for all 
we have 
.
A function is said to be continuous on an interval if it is continuous in each of the interval's points.
An alternative definition using limits is 
.
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