This book examines an abstract mathematical theory, placing special emphasis on results applicable to formal logic. If a theory is especially abstract, it may find a natural home within several of the more familiar branches of mathematics. This is the case with the theory of closure spaces. It might be considered part of topology, lattice theory, universal algebra or, no doubt, one of several other branches of mathematics as well. In our development we have treated it, conceptually and methodologically, as part of topology, partly because we first thought ofthe basic structure involved...
This book examines an abstract mathematical theory, placing special emphasis on results applicable to formal logic. If a theory is especially abstract...
Lighthouse Rainbows utilizes a range of creative styles so that readers will feel like they are part of a particular poem. The book covers the trials and tribulations of life, the sweetness of nature, and our love for lyrics that can be put to enjoyable musical melodies.
Lighthouse Rainbows utilizes a range of creative styles so that readers will feel like they are part of a particular poem. The book covers the trials ...
Lighthouse Rainbows utilizes a range of creative styles so that readers will feel like they are part of a particular poem. The book covers the trials and tribulations of life, the sweetness of nature, and our love for lyrics that can be put to enjoyable musical melodies.
Lighthouse Rainbows utilizes a range of creative styles so that readers will feel like they are part of a particular poem. The book covers the trials ...
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert's program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this...
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other are...
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other areas of foundational research. This volume features English translations of 14 papers Pasch published in the decade 1917-1926. In them, Pasch argues that geometry and, more surprisingly, number theory are branches of empirical science; he provides axioms for the combinatorial reasoning essential to Hilbert's program of consistency proofs; he explores "implicit definition" (a generalization of definition by abstraction) and indicates how this...
Moritz Pasch (1843-1930) is justly celebrated as a key figure in the history of axiomatic geometry. Less well known are his contributions to other are...
This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Godel's...
This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mat...
This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Godel's...
This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mat...
