• 2.3: Statements Containing Multiple Quantifiers

    • University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic and Numbers: Logic" URL

      Read from example 11 up to Exercises for Section 2 on pages Lo-16 - Lo-19. These readings also apply to topics in subunits 2.3.1 and 2.3.2. The examples work with multiple quantifiers and pertain to translation between logic and math and English domains.

      The direction of the translation from formal to informal language is typically done to communicate a result obtained from logic, back to the language in which the problem was specified.

      Translation from a natural language to logic, is done to apply logic to a problem in some other discipline or everyday task (e.g. history, science; making a decision, debating). Furthermore, in applying logic, we also find it useful to translate from logic to logic (to transform a statement into a more convenient form), and to translate from a natural language to a natural language to simplify translation to logic.

    • Definition of a Limit URL

      Read this text in its entirety to better understand the definition of a limit and primarily to illustrate the use of the notation from this unit.

      Limits are studied in continuous mathematics, such as the differential and integral calculus, and in analysis. Discrete mathematics (which is studied in discrete structures) provides the concepts that are used in defining topics in continuous mathematics. This is illustrated with the reading for this topic.