The whole interval is produced by adding dust to itself! Footnote 1

And God said, Let us make man in our image, after our likeness; male and female created She them. But they misbehaved. So She sent Her prophets to correct them. She gave Moses tablets of commandments: a simplified list of rules to live by, in essence be good people. But there were those who did not believe. So She sent Jesus with a path to her embrace and a message clear and simple: be kind to each other. But there were those who did not believe. She sent Muhammad with Her exact words: lessons and laws wrapped in divine poetry, words that floated from the lips of men and women up to heaven itself. Still, there were those who did not believe. Finally after trying, and trying, and trying, once and again, She reached out to provide proof of Her existence. She reached out to give us evidence so irrefutable, so concrete, that none could ever doubt Her. And so She whispered to a man, a prince of the mind, the young and gifted Georg Cantor. “Look at what is left when all has been removed and there you will see my shadow: a set of measure zero, a perfect set. Sparse like a pinch of sand spread among the stars is my shadow, nowhere dense and completely disconnected yet vast enough to cover all the globe. Wherever you look, my shadow is there hidden in all compact sets. Take my shadow in each hand, then put your hands together and Behold! From pinches of nothing the whole segment will return. Just as I created you from dust, you too from dust can now create.” And yet still there are those who do not believe.