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@@ -16,7 +16,7 @@ Infinity, of course. So to perform a meaningful check that the set of nice perio
 
 For example, the open interval $(-\pi,\pi)$ has the same cardinality as $\mathbb R$. To see this, take the interval and bend it into a semicircle, then balance it on the real line. To find the point on the real line corresponding to a given number in the interval/on the semicircle, $\theta \in (-\pi,\pi)$, draw the straight line emanating from the centre of the circle at an angle $\theta$ with the vertical; it hits $\theta$ on the semicircle and its partner $x$ on the real line. Explicitly, the map takes $\theta \mapsto \tan \theta$.
 
-![alt text](/stereographic circle.jpg)
+<center>![](/stereographic circle.jpg)</center>
 
 There are, however, fewer natural numbers in $\mathbb N = \{1,2,3,\dots\}$ than there are real numbers in $\mathbb R$. Suppose to the contrary that it is possible to list the real numbers, or even just those in the interval $(0,1)$. Write that list down in binary, forming a big block extending infinitely downward (each row is a number), and to the right (the binary digits of each number). Read off the digits on the diagonal to get a number $x=0.010100110101110101011\dots$. Now toggle every digit of that number to get a new number $y$, say $0.101011001010001010100\dots$. This number $y$ is not anywhere on the list--it disagrees with the $n^{th}$ number on the list in its $n^{th}$ digit. Hence the list was incomplete.