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We already saw a square (one of plane figures) is
given by
with absolute function |x|.
There is an another equation using which is given by
in other work of mine (see ``plane figure equations'').
This provides a resort to study discontinuous functions
with linear calculus.
The expedient is as follows.
- Suppose the problem in question contains discontinuous functions.
- Express discontinuous functions as a continuous functions
with parameters (as n in equation (2)) so as to approach
the discontinuous functions under the limit of the parameter.
We call them pseudo functions.
- Study the problem with the continuous pseudo functions instead of
the discontinuous functions.
- Take a limit of introduced parameters in the results
of pseudo functions.
Next: Examples for and
Up: Discontinuous functions
Previous: Discontinuous functions
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