Properties of well-ordered sets, such as point-set topologies, are often demonstrated using the transfinite form of this technique.
Properties of well-ordered sets, such as point-set topologies, are often demonstrated using the transfinite form of this technique. George Polya used the example of a horse of a different color to illustrate the subtleties of this technique. The strong form of this technique allows one to assume that a statement is true for all values in between zero and k. This technique, which is closely related to recursion, begins by proving a (*) base case and then assuming the namesake hypothesis is true for n; subsequently, one must demonstrate that a statement holds for the n + 1 case. For 10 points, name this kind of mathematical proof in which some statement is demonstrated to be true for all natural numbers.
Properties of well-ordered sets, such as point-set topologies, are often demonstrated using the transfinite form of this technique.
induction [or deductive reasoning; or word forms; prompt on proofs]