• Jun 23rd 2011, 12:14 PM
taypen
hello,

i got continuous function on $[0,1]$ such that $f(0) = f(1)$ i need to prove that exist "a" such that $f(a) = f(a+0.5)$
$a\in \left[0,\frac{1}{2}\right]$

your help would be much appreciated!
• Jun 23rd 2011, 02:20 PM
emakarov
Emakarov is correct. Look at the example at the bottom of the article concerning real world applications. Your problem is just a slight variation: consider the function $g(t)=f(t)-f(t+0.5)$.