The screen went white. Not the white of a dead pixel, but the pure, axiomatic white of a blank sheet of infinite paper. Then the text reformed. It was no longer Backhouse's voice. It was his own.
“Let E be the set of all possible versions of Elias. Let R be the relation ‘is afraid of.’ Prove that R is not an equivalence relation because it is not reflexive: no Elias is afraid of himself until now.” pure mathematics by j.k backhouse pdf
He slammed the laptop shut. The wall went back to being a wall. The air went back to being air. But his reflection in the dark screen was still looking at him from an angle he wasn't sitting at. And in its hand, it held a green book that did not exist. The screen went white
The book was a ghost. Elias knew it the moment he saw the listing on an old forum: “Pure Mathematics by J.K. Backhouse – PDF scan – eternal recursion included free.” It was no longer Backhouse's voice
He tried to think of his mother’s face. Instead, he saw a function: f: {memories} → {emotional states} . It was not injective. Many memories mapped to the same dull ache.
By dawn, he had finished Chapter 7: Functions. He looked up from his laptop. His dorm room was the same—the stained coffee mug, the pile of unwashed laundry—but it wasn't. The wall on the left was no longer a solid surface. It was a set of paint molecules, each one a discrete element, each one related to its neighbor by a weak van der Waals relation. The air was not air; it was a field of continuous points, an uncountable infinity.
Panic should have set in. Instead, a calm, terrible curiosity took hold. He scrolled to the final chapter: “The Axiom of Choice & Beyond.” A handwritten note in the scan said: “Reader, you are being observed by the set of all sets that do not contain themselves. Do not look back.”