An introduction to Georg Cantor’s transfinite paradise
&quot;<i>Proof that |ℝ²| = |ℝ|
It suffices to prove that the set of all pairs (x,y), 0 &lt; x,y &lt; 1 can be mapped bijectively onto (0,1]. Consider the pair (x,y) and write x,y in their unique non-terminating decimal expansion as in the following example:...</i>&quot;<p>I hadn&#x27;t seen this proof before. I assume the &quot;unique non-terminating decimal expansion&quot; uses the 0.999... = 1.0... shenanigan due to &quot;Since neither x nor y exhibits only zeroes from a certain point on...&quot;<p>Further, &quot;<i>Reportedly, Kronecker disagreed fundamentally with the thrust of Cantor’s work on set theory because, among other reasons, it asserted the existence of sets satisfying certain properties without giving examples of specific sets whose members satisfied these properties. Kronecker also only admitted mathematical concepts if they could be constructed in a finite number of steps from the natural numbers, which he took for a given.</i>&quot; Kronecker was a constructivist?!