Fun with infinite sets

Imagine the graph of function the f(x)=sin(x).f(x)=\sin(x). The domain of this function is the set of all real numbers R.R.

Consider the three sets

  • A={xRsin(x)=1}A=\left\{ x\in \mathbb R|\sin(x)=-1 \right\}
  • B={xRsin(x)=0}B=\left\{ x\in \mathbb R|\sin(x)=0 \right\}
  • C={xRsin(x)=1}.C=\left\{ x\in \mathbb R|\sin(x)=1 \right\}.

Which of them has the largest cardinality?


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