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Understanding numbers requires both approximation and exactness from "summary" of The Number Sense by Stanislas Dehaene
Numbers inhabit a dual world of precision and fluidity. On one hand, there exists the realm of exact values, where integers and rational numbers provide a clear, unambiguous representation. This precision is essential for tasks requiring absolute accuracy, such as scientific calculations or financial transactions. In these contexts, the exactness of numbers serves as a foundation upon which decisions are made and predictions are formed. Conversely, the cognitive grasp of numerical concepts often begins with a more approximate understanding. Humans possess an innate ability to estimate quantities, a skill evident even in young children and non-human animals. This approximate sense allows individuals to navigate their environments, making quick judgments about size, distance, and quantity without needing exact figures. The ability to discern whether a group of objects is "more" or "less" than another, for instance...
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