Let S = {tan(k) : k = 1,2,...}. Find the set of limit points of S on the real line.
The answer to this question is the whole real line could someone explain why this is true?
Topoltergeist wrote:For each real numbers $x,y \in \mathbb{R} we define an equiv relation by
x~y if there exists an integer n such that x = 2*\pi n + y
Naturally, for every real number $x$, there is a unique number $y \in [0,2 \pi)$ such that $x~y$. We define $y = x mod 2 \pi$
If the set is finite, then there would be integers $n,m$ such that $n = m * (2\pi)$.....
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