In a circle, each $x$-value can be mapped to one $y$-value above and one $y$-value below the $x$-axis.
Each $y$-value can be mapped to the one $x$-values on the left and another on the right of the $y$-axis.
Considering the fact that the $x$-values constitute the domain and the $y$-values are the range, would a circle not be a many-to-many mapping?
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