# Thread: Continuous Functions and The intermediate value theorem

1. ## Continuous Functions and The intermediate value theorem

Suppose that f is a continuous function on the interval [0,1] and that f(0) = f(1).

If n is an integer greater than 2, show that:
f(a) = f(a + (1/n) ) for some $a \in [0,1 - (1/n)]$.

How would I approach this question? Would I need to apply mathematics induction?

Thanks, any help will be highly appreciated.

2. ## Help

See Latest Posting

3. Hi there, thanks for the reply. I'm still having trouble with the above question.

Is it correct to do this by induction?
By showing it is true for n = 3, assume n = k is true and prove n = k + 1 is true.

But, how would I go about proving n = k + 1 if n = k is true (by induction)?

Also, is there any other alternative methods of doing this question?

Thanks

4. See the very latest posting

5. See the very latest posting

6. ## getting closer

See the latest following Post ignore this one

7. Finally--- see the attachment for the proof--with a big debt to Plato
for showing the direction to go