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What was Leibniz's take on "impossible" numbers? Gottfried Wilhelm Leibniz (1646-1716) described imaginary roots, negative numbers, and infinitesimals as useful fictions. Leibniz often used "infinite number" in the sense of what we would refer to today as "infinite cardinality" (contradictory in Leibniz's view), indicating that he used the term "infinite number" in a generalized sense. Alice argues that Leibniz's exchange with Bernoulli about infinite series shows that Leibniz viewed infinitesimals and infinite quantities as contradictory.[17] Bob notes that Leibniz stresses the distinction between infinite cardinality and infinite quantity (reciprocal of infinitesimals). [Extracted from the article]