Question: is it obvious that if the orbit avoids the interval, then there must be some integer n n such that f n ( a )

is it obvious that if the orbit avoids the interval, then there must be some integer n n such that f n ( a ) = a f n (a)=a, meaning x + n a x ( m o d 1 ) x+nax(mod1). or do i have to also prove this

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