A proof of a formula on limits based on the epsilon-delta definition. An example is the following proof that every linear function (
) is continuous at every point
. The claim to be shown is that for every
there is a
such that whenever
, then
. Now, since
(1)
| |||
(2)
| |||
(3)
|
it is clear that
(4)
|
Hence, for all ,
is the number fulfilling the claim.