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Hi my name is Scott Howe, and I am double majoring in philosophy and computer science I also have a background in mathematics in theoretical physics First became interested in programming in fourth grade when I wanted to do nothing but make video games discovered hue basic and right away began to learn the ropes of game programming my interest in programming also led to my learning trigonometry to develop a 3d engine in a few years Hope to be developing business software and writing a few modules applicable tooth the academic and gaming worlds Also hope to be an author and write about several subjects including mathematical philosophy my presentations on Z notation which is a useful way of describing the behavior of a software system that is based on our current understanding of mathematics I found said to be very inspired and would note surprised if it becomes a highly successful specification language let's get started standing z notation this brief introduction will provide an overview of what Z is about and offer an example of how to use Z to model a system what is Z is a model-based notation that was conceived in the late 1970sthrough collaborative projects between Oxford University and its industrial partners an official Z standard was released in 2002Z is not a programming language it does not compile into executable code, and it does not run in an interpreter the purpose of Z is to describe the behavior of a system such as a software application in the language of modern mathematics the predominant foundation of modern mathematics also used in Z isZermelo Frankel set theory so let's begin by looking at ZermeloFraenkel set theory melt Frankel set theory commonly abbreviated OF or OF c is a language used to describe the properties of sets that is aggregates or collections of objects Carmelo Frankel set theory has become so mainstream as a foundation of mathematics that it underlies every branch including algebra calculus and discrete mathematics as modern physics is based on a mathematical description of nature it also has its ultimate basis and Carmelo Frankel set theory sir meloFraenkel set theory is based on seven core axioms these axioms are used to deduce the truth of further mathematical statements which form the basis of all subjects in mathematics taught in schools all of them are stated in the symbolic language of first-orderpredicate logicality×39’s review symbolic logic contains subjects and predicates which express relationships between objects and their properties logical negation which expresses the untruth of statements logical connectives such sand or and implies which join statement sand well-defined ways and quantifiers which use a variable to express general laws or statements of existence now let's take a look at the seven core axioms of Carmelo Frankel set theory the axiom of extensional states that any two sets with the same members' art be considered is equal the sum axiom states that for any set an of other sets one...
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