proof of intermediate value theorem
We first prove the following lemma.
If is a continuous function with then there exists a such that .
Define the sequences and inductively, as follows.
We note that
But we have and so that . Furthermore we have , proving the assertion.
Set where . satisfies the same conditions as before, so there exists a such that . Thus proving the more general result.
|Title||proof of intermediate value theorem|
|Date of creation||2013-03-22 12:33:56|
|Last modified on||2013-03-22 12:33:56|
|Last modified by||yark (2760)|