Ted French, from an informed point view, summarizes the set theory; highlighting most relevant and commonly applicable aspects of the sets as outlined in discrete mathematics. The author dwells on aspects of the set theory that mainly used in computer science in defining variables and building functions. To achieve this, in particular, the article discusses set overview, set notation, element order and repetition, sets and ellipses. Special sets, roster verses descriptive form of representing sets, set builder form of representing sets, shorthand characters and sets and Venn diagrams. The author goes further to define a set a list or a collection of objects. Great emphasis is accorded set notations. That is Venn diagrams, set builder notation, roster form and descriptive way of representing sets. In the process of achieving this, discrete mathematics symbols and notations of representing logical statements and numbers are brought forward. This includes , among many other symbols. For instance, represents an empty set while is a representation of real numbers.
The source is recent, credible and relevant. Inasmuch as the source is relevant and credible, the content of the source is very shallow. The emphasis has been given to definition and symbols used in the topic rather than presenting deeper content of the topic at hand. Completion of the part of this assignment that requires this information could not be satisfactorily be completed without consulting other sources.
The article is a tutorial that focuses on the number systems; binary, decimal and hex conversion. The author, Panos Georgiadis, use explanations and numerical examples to illustrate how to carry out conversions between binary, decimal and hex. For instance, an example is given on how to convert 343, which is a decimal number to binary notation. The tutorial explains the meaning of binary, decimal and hex number system. Besides, a greater emphasis is given to binary to decimal conversion, decimal to binary conversion, hex to binary conversion and vice versa, hex to decimal conversion and vice versa. For each conversion, a numerical illustration is given to show how to carry out the conversion.
The source is recent. Panos is a renowned writer in the area of Information Technology and has
written a myriad of articles for many IT websites. For that reason, the source is credible and relevant. Besides, the information is enough to meet the requirement of this part of the assignment.
This is an article about set theory that was written by Robert Stoll and Herbert Enderton. The two authors state that set theory is a branch of mathematics that specializes in the properties of a well-specified group of objects may or may not mathematical value. Both numbers and functions, and how they are used in set theory are highlighted. Additionally, the history and evolution of set theory are explained. Another aspect of the set theory that is given much attention is the application of the sets. Some areas of application such religion, philosophy and geometry are discussed. The authors give an emphasis on the na?ve set theory where the fundamental set concepts are highlighted. It is noted that na?ve theory has a unique definition that assumes that a set is a group of objects called elements that are taken as single objects.
The article concentrates on a very narrow part of set theory thus its content is too shallow. Consequently, the source cannot independently support meeting of the assignment’s objectives. Thus the source must be used together with other sources to get relevant information needed for the completion of the exercise. The source both relevant, recent and credible.
Stephen Simpson writes about logic and mathematics. The article borrows information from other sources to explain various aspects of logic and mathematics. The main aspects highlighted under logic are Aristotlean logic and the predicate calculus. Under foundation of mathematics, the topics discussed are Euclidean geometry and formal theories of mathematics. On the other hand, Plato and Aristotle, the 20th Century and the future are discussed under the philosophy of mathematics. An important aspect discussed under Aristotlean logic is the law of syllogism.
While the source is relevant and credible, it is not recent. It was written in 1999; which is 18 years ago. Additionally, the information is shallow and extra information must be sought to meet the requirements needed for the law of syllogism.
The article explains the meaning and determination of the set theory. Cardinality is defined as the number of elements in a set. Besides definition, two types of sets are discussed; these are finite and infinite cardinalities. Under each, numerical examples are given support the explanation. Besides, the main aspects of the article, cardinality, minor subtopics such as diagonalization and set mapping are also explained.
The article is recent, relevant and credible. The information presented is credible because it agrees with other information written by other authors in various books. Additionally, the information given is enough to meet the requirement of the assignment of cardinality.