How real are real numbers? (2004)
<i>&quot;So, in Borel’s view, most reals, with probability one, are mathematical fantasies, because there is no way to specify them uniquely.&quot; (Paraphrasing, because there are only countably many possible math papers that might describe a number.)</i><p>I think Borel has confused names with things. The fact that we can only write down only countably many <i>expressions</i> for numbers doesn&#x27;t mean that there are numbers that we may never write expressions for - only that in a single symbolic system we can&#x27;t have expressions for all of them <i>at once</i>.<p>Besides, if you confuse extant with useful you might end up believing that some random large integers aren&#x27;t &quot;there!&quot;