Numbers

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book Numbers by Henry F. De Francesco, Xlibris US
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Henry F. De Francesco ISBN: 9781503521513
Publisher: Xlibris US Publication: February 12, 2015
Imprint: Xlibris US Language: English
Author: Henry F. De Francesco
ISBN: 9781503521513
Publisher: Xlibris US
Publication: February 12, 2015
Imprint: Xlibris US
Language: English

In preparing this monograph I had three objectives. First, I wanted to introduce the reader to some topics in mathematics that seldom receive coverage in typical high school and college math programs. The topics include axioms, sets, logic, truth tables and plausible reasoning. In the sections on logic and plausible reasoning, I wanted the reader to see how to transition from formal (mathematical) logic to plausible logic when analyzing the reliability of a source and the credibility of its information content. Readers whose formal education did not cover these topics were not given the opportunity to develop the skills necessary to compete successfully in the world of finance, business and management. These readers will find the information on sets, logic, truth tables and plausible reasoning especially useful. Included are examples that show how the new analysis skills can help analysts draw conclusions and make important decisions from subjective information supplied by less than reliable sources. Second, I wanted the reader to see how subjects in the foundations area of mathematics are used to develop the real number system and its extension through transfinite cardinal numbers. The development of the number system starts with a description of the history of numbers. Readers will find the history both interesting and understandable. The real number continuum is identified as consisting of seven sets of numbers. Each set of numbers can stand alone. The number sets include the simple to understand natural numbers to the more abstract transcendental numbers. Each set is defined and included in a vocabulary consisting of the natural numbers N, integers Z, the rational numbers F, the algebraic numbers A, transcendental numbers T, irrational numbers I, and real numbers R. Venn diagrams are used to explain the relationships existing among the seven sets. The relationships allow the reader to understand the role played by sets and logic in the development of the number system. Included In the development of the real number system are examples of base2 numbers and the algorithms used to convert between base 2 and base 10 numbers. Power Sets are introduced to show how the size of sets can be increased exponentially beyond the cardinal numbers N0 and c. Finally, through exponentiation, cardinal numbers are generated beyond the N0< c < f sequence. Third, I wanted this monograph to appeal to those adults, and their children, who have an anti-math bias. This bias is exhibited as innumeracy or an aversion to math. In either case, those afflicted find it difficult to compete against the mathematically literate in the world of business, finance and technology. Through this monograph I attempt to address this anti-math bias. The reader is introduced to the language of sets, logic and plausible reasoning. While these subjects are part of the foundations of mathematic, they are also subjects taught in Philosophy departments without math prerequisites. The reader is then shown how axioms, sets and logic are applied in the development of the number system. The subject of numbers is made intelligible for a broader spectrum of readers through the use of verbal descriptions and graphics, rather than equations, wherever possible. To achieve a continuous flow of understandable subject matter, the more tenuous procedures and methods of mathematics are explained in 6 appendices. Through understanding how math works at the fundamental level, and not having to work at math, the intelligent readers anti- math bias should be reduced, if not, eliminated.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

In preparing this monograph I had three objectives. First, I wanted to introduce the reader to some topics in mathematics that seldom receive coverage in typical high school and college math programs. The topics include axioms, sets, logic, truth tables and plausible reasoning. In the sections on logic and plausible reasoning, I wanted the reader to see how to transition from formal (mathematical) logic to plausible logic when analyzing the reliability of a source and the credibility of its information content. Readers whose formal education did not cover these topics were not given the opportunity to develop the skills necessary to compete successfully in the world of finance, business and management. These readers will find the information on sets, logic, truth tables and plausible reasoning especially useful. Included are examples that show how the new analysis skills can help analysts draw conclusions and make important decisions from subjective information supplied by less than reliable sources. Second, I wanted the reader to see how subjects in the foundations area of mathematics are used to develop the real number system and its extension through transfinite cardinal numbers. The development of the number system starts with a description of the history of numbers. Readers will find the history both interesting and understandable. The real number continuum is identified as consisting of seven sets of numbers. Each set of numbers can stand alone. The number sets include the simple to understand natural numbers to the more abstract transcendental numbers. Each set is defined and included in a vocabulary consisting of the natural numbers N, integers Z, the rational numbers F, the algebraic numbers A, transcendental numbers T, irrational numbers I, and real numbers R. Venn diagrams are used to explain the relationships existing among the seven sets. The relationships allow the reader to understand the role played by sets and logic in the development of the number system. Included In the development of the real number system are examples of base2 numbers and the algorithms used to convert between base 2 and base 10 numbers. Power Sets are introduced to show how the size of sets can be increased exponentially beyond the cardinal numbers N0 and c. Finally, through exponentiation, cardinal numbers are generated beyond the N0< c < f sequence. Third, I wanted this monograph to appeal to those adults, and their children, who have an anti-math bias. This bias is exhibited as innumeracy or an aversion to math. In either case, those afflicted find it difficult to compete against the mathematically literate in the world of business, finance and technology. Through this monograph I attempt to address this anti-math bias. The reader is introduced to the language of sets, logic and plausible reasoning. While these subjects are part of the foundations of mathematic, they are also subjects taught in Philosophy departments without math prerequisites. The reader is then shown how axioms, sets and logic are applied in the development of the number system. The subject of numbers is made intelligible for a broader spectrum of readers through the use of verbal descriptions and graphics, rather than equations, wherever possible. To achieve a continuous flow of understandable subject matter, the more tenuous procedures and methods of mathematics are explained in 6 appendices. Through understanding how math works at the fundamental level, and not having to work at math, the intelligent readers anti- math bias should be reduced, if not, eliminated.

More books from Xlibris US

Cover of the book The Piker Street Drop and Other Pieces by Henry F. De Francesco
Cover of the book A–Z My All-Time Favorites by Henry F. De Francesco
Cover of the book Presidential Foreign Language Trivia by Henry F. De Francesco
Cover of the book Imperfect Family: Setting Free Skeletons of Kinship Neglect by Henry F. De Francesco
Cover of the book That's Not What I Heard! by Henry F. De Francesco
Cover of the book The Lost Sister by Henry F. De Francesco
Cover of the book Sit with It: the Truth Behind Weight Loss by Henry F. De Francesco
Cover of the book Ghosts of Makara by Henry F. De Francesco
Cover of the book A Diplomat in Guangzhou (Canton) by Henry F. De Francesco
Cover of the book Clyde Strikes Back by Henry F. De Francesco
Cover of the book Hope Beyond Shadows of Pain by Henry F. De Francesco
Cover of the book Black Star over Hollywood by Henry F. De Francesco
Cover of the book The Gifted One by Henry F. De Francesco
Cover of the book Macbeth for Murderers by Henry F. De Francesco
Cover of the book Everybody for Everybody: Truth, Oneness, Good and and Beauty for Everyone's Life, Liberty and Pursuit of Happiness Volume 1 by Henry F. De Francesco
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy