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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 .
How would I approach this question? Would I need to apply mathematics induction?
Thanks, any help will be highly appreciated.
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