Question

define a function \(\gamma:\mathbb{N}\to\mathbb{N}\) such that every \(\gamma(x)=n\) has infinitely many solutions\[\]i am infinitely stuck on this problem. i need fresh ideas :(((

Answer 1

won't a periodic function work?

Answer 2

i thought the same but then it would have to be a periodic function with an infinite amplitude... wait a moment

Answer 3

\[\gamma(x)=\left \lceil \tan(x) \right \rceil\]could have worked if it was surjective

Answer 4

Just making sure, N-> [1,infinity] and integer values only, right?

Answer 5

that's correct; it's a function from [1, infinity) to [1, infinity).

Answer 6

one idea could be a function that looks something like this