4.16.24 21st Century Movements for Black Lives.pptx
Induction
1. INDUCTION As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise – By what course of calculation can these results be arrived at by the machine in the shortest time? - Charles Babbage, 1864
12. Well-Formed Formulas T is a wff F is a wff p is a wff for any propositional variable p If p is a wff, then ( p) is a wff If p and q are wffs, then (p q) is a wff If p and q are wffs, then (p q) is a wff For example, a statement like (( r) (p r)) can be proven to be a wff by arguing that ( r) and (p r) are wffs by induction and then applying rule 5. Note: we have three recursive/construction rules to create new elements. 03/12/11 Basic Cases Recursive Step