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Mathematics 19 Online
OpenStudy (anonymous):

definition for continuity?

OpenStudy (anonymous):

\[f(x) = \frac{1}{x - 1 } \] the function is discontinuous at x=1

OpenStudy (anonymous):

i just need a written definition for what it is

OpenStudy (anonymous):

A function \(f:\mathbb{R}\to\mathbb{R}\) is continuous at some point \(a\) if \(\lim_{x\to a}f(x) = f(a)\)

OpenStudy (anonymous):

Continuity means that the value of f(x) exists for all values of x

OpenStudy (anonymous):

thank you snaef999

OpenStudy (anonymous):

The function is continuous if it is continuous at all points.

OpenStudy (anonymous):

snaef999 thats incorrect.

OpenStudy (anonymous):

on a given interval..?

OpenStudy (anonymous):

A function can be defined for all values yet fail to be continuous. See point discontinuity or step discontinuity.

OpenStudy (anonymous):

Yes that is true.

OpenStudy (anonymous):

A correct definition of continuity requires the concept of limit.

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