This paper argues that there is a precise, mathematical notion of “continuity” at work in the “Ithaca” chapter of Ulysses, which Joyce drew from Bertrand Russell’s Introduction to Mathematical Philosophy (1919), and that this concept helps clarify the continuity we find in Joyce’s “logical fictions.” Joyce copied both “continuity” and “logical fictions” from Russell’s Introduction, along with dozens of other phrases from the book, many of which he worked into “Ithaca.” Joyce’s use of Russell has been remarked on before, but this paper examines Joyce’s notes from a logical point of view, observing that Russell’s book is as much an introduction to logic as mathematics. Joyce’s results in logic and mathematics at Belvedere College and University College Dublin show that he had greater facility in these subjects than is usually assumed, which helps explain his interest in the logico-mathematical concepts Russell expounds. The way Joyce inserted terms like “continuity” into “Ithaca” (U 17.1065) suggests that he was using them in Russell’s sense, but at the same time, the literary appropriation of these terms indicates that Joyce was at least as interested in fictionalizing logic as in the logic of his fiction.