A Function with a Jump Discontinuity

​
slope
1.5
y
0
= f(​
x
0
​)
0.4
determine ϵ
0.25
choose δ
0.1
find x
0.17
vertical/horizontal lines
show text
This Demonstration gives an example of a function with a jump discontinuity. A function
f
defined in some neighborhood of
x
0
is discontinuous at
x
0
if there exists
ϵ>0
such that for each
δ>0
, there exists an
x
such that
|x-
x
0
|<δ
and
|f(x)-f(
x
0
)|≥ϵ
.

External Links

Continuous Function (Wolfram MathWorld)
Uniform Continuity

Permanent Citation

Izidor Hafner
​
​"A Function with a Jump Discontinuity"​
​http://demonstrations.wolfram.com/AFunctionWithAJumpDiscontinuity/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011