Reasoning about Infinity

Roles: infinite-sequence, limit, convergence, divergence, countable, uncountable, asymptote

The domain of reasoning about unbounded quantities, infinite processes, and their counterintuitive properties. As a target domain, reasoning about infinity is where metaphors from probability, set theory, and analysis land when people try to make sense of the gap between the finite and the unbounded. Concepts like “almost surely,” convergence, and the difference between countable and uncountable infinities structure how we think about limits, potential, and the long run. The frame’s danger is that infinity is routinely invoked without its formal constraints — “given enough time” sounds modest until you calculate how much time “enough” actually requires.

Applied To This Frame (1)