finite mathematics in nLab
Finite mathematics is the mathematics of finite sets. The term is sometimes used more broadly for discrete mathematics. We may say that finite mathematics is mathematics done internal to the category FinSet of finite sets or the mathematics of Fin Set itself. The latter (but not the former) includes the basic arithmetic of natural numbers, since these are the cardinalities of finite sets; we can go as far as rational numbers this way, but not real numbers. Finite mathematics also includes a great deal of combinatorics, basic algebra, and elementary formal logic, although not many advanced topics. In the foundations of mathematics and in philosophy of mathematics, finitism is the philosophical sentiment that one “should” do only finite mathematics. In a weak sense, one should not assume the axiom of infinity; in a strong sense, one should even deny it by an axiom of finiteness. This makes it impossible to do analysis as we normally understand it. Finitism (in the weak sense of not acc
finite mathematics in nLab nLab finite mathematics Skip the Navigation Links | Home Page | All Pages | Latest Revisions | Discuss this page | Finite mathematics Finite mathematics Idea Finitism The mathematics of FinSet Neutral finite mathematics π \pi -finite mathematics See also References Idea Finite mathematics is the mathematics of finite sets . The term is sometimes used more broadly for discrete mathematics . We may say that finite mathematics is mathematics done internal to the category FinSet of finite sets or the mathematics of Fin Set \Fin\Set itself. The latter (but not the former)
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