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asked Does mathematical induction assume that non-negative integers are infinite?
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comment Space filling paths
Yes that was my motivation: Cantor's diagonal argument and its implication that there are as many points in a line as in a plane or any other subset of $R^n$. I did not know that onto transformations from $R$ to $R^2$ where possible; I was under the impression that it was impossible, which is why I considered my transformation paradoxical, but if what you claim is true then there really is no paradox. I find it even more surprising that bijective mappings from $R$ to $R^2$ exist.