Skip to main content
Springer Nature Link
Log in

A Formal Background to Mathematics

Logic, Sets and Numbers

  • Book
  • © 1979

Overview

Authors:
  1. Robert Edwards

    1. Institute of Advanced Studies, The Australian National University, Canberra, Australia

Part of the book series: Universitext (UTX)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

') var buybox = document.querySelector("[data-id=id_"+ timestamp +"]").parentNode var buyboxMaxSingleColumnWidth = 480 ;[].slice.call(buybox.querySelectorAll(".buying-option")).forEach(initCollapsibles) function initCollapsibles(buyingOption, index) { var toggle = buyingOption.querySelector(".buying-option-price") buyingOption.classList.remove("expanded") var form = buyingOption.querySelector(".buying-option-form") var priceInfo = buyingOption.querySelector(".price-info") if (toggle && form && priceInfo) { toggle.setAttribute("role", "button") toggle.setAttribute("tabindex", "0") toggle.addEventListener("click", function (event) { var expandedBuyingOptions = buybox.querySelectorAll(".buying-option.expanded") var buyboxWidth = buybox.offsetWidth ;[].slice.call(expandedBuyingOptions).forEach(function(option) { if (buyboxWidth <= buyboxMaxSingleColumnWidth && option != buyingOption) { hideBuyingOption(option) } }) var expanded = toggle.getAttribute("aria-expanded") === "true" || false toggle.setAttribute("aria-expanded", !expanded) form.hidden = expanded if (!expanded) { buyingOption.classList.add("expanded") } else { buyingOption.classList.remove("expanded") } priceInfo.hidden = expanded }, false) } } function hideBuyingOption(buyingOption) { var toggle = buyingOption.querySelector(".buying-option-price") var form = buyingOption.querySelector(".buying-option-form") var priceInfo = buyingOption.querySelector(".price-info") toggle.setAttribute("aria-expanded", false) form.hidden = true buyingOption.classList.remove("expanded") priceInfo.hidden = true } function initKeyControls() { document.addEventListener("keydown", function (event) { if (document.activeElement.classList.contains("buying-option-price") && (event.code === "Space" || event.code === "Enter")) { if (document.activeElement) { event.preventDefault() document.activeElement.click() } } }, false) } function initialStateOpen() { var buyboxWidth = buybox.offsetWidth var narrowBuyboxArea = buyboxWidth <= buyboxMaxSingleColumnWidth var allOptionsInitiallyCollapsed = buybox.className.indexOf("all-options-initially-collapsed") > -1 ;[].slice.call(buybox.querySelectorAll(".buying-option")).forEach(function (option, index) { var toggle = option.querySelector(".buying-option-price") var form = option.querySelector(".buying-option-form") var priceInfo = option.querySelector(".price-info") if (allOptionsInitiallyCollapsed || narrowBuyboxArea && index > 0) { toggle.setAttribute("aria-expanded", "false") form.hidden = "hidden" priceInfo.hidden = "hidden" } else { toggle.click() } }) } initialStateOpen() if (window.buyboxInitialised) return window.buyboxInitialised = true initKeyControls() })()

Other ways to access

Licence this eBook for your library

See More

Institutional subscriptions

About this book

§1 Faced by the questions mentioned in the Preface I was prompted to write this book on the assumption that a typical reader will have certain characteristics. He will presumably be familiar with conventional accounts of certain portions of mathematics and with many so-called mathematical statements, some of which (the theorems) he will know (either because he has himself studied and digested a proof or because he accepts the authority of others) to be true, and others of which he will know (by the same token) to be false. He will nevertheless be conscious of and perturbed by a lack of clarity in his own mind concerning the concepts of proof and truth in mathematics, though he will almost certainly feel that in mathematics these concepts have special meanings broadly similar in outward features to, yet different from, those in everyday life; and also that they are based on criteria different from the experimental ones used in science. He will be aware of statements which are as yet not known to be either true or false (unsolved problems). Quite possibly he will be surprised and dismayed by the possibility that there are statements which are "definite" (in the sense of involving no free variables) and which nevertheless can never (strictly on the basis of an agreed collection of axioms and an agreed concept of proof) be either proved or disproved (refuted).

Similar content being viewed by others

Explore related subjects

Discover the latest articles, books and news in related subjects.

Table of contents (6 chapters)

  1. Front Matter

    Pages I-XXXIV
    Download chapter PDF

  2. Logic and Formal Theories

    • Robert Edwards
    Pages 1-134

  3. Elements of Set Theory

    • Robert Edwards
    Pages 135-276

  4. Relations

    • Robert Edwards
    Pages 277-339

  5. Functions

    • Robert Edwards
    Pages 340-467

  6. Natural Numbers and Mathematical Induction

    • Robert Edwards
    Pages 468-637

  7. Concerning Z, Q and R

    • Robert Edwards
    Pages 638-721

  8. Back Matter

    Pages 722-935
    Download chapter PDF
Back to top

Authors and Affiliations

  • Institute of Advanced Studies, The Australian National University, Canberra, Australia

    Robert Edwards

Accessibility Information

PDF accessibility summary

This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at [email protected] if you require assistance or an alternative format.

Bibliographic Information

  • Book Title: A Formal Background to Mathematics

  • Book Subtitle: Logic, Sets and Numbers

  • Authors: Robert Edwards

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4612-9984-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1979

  • Softcover ISBN: 978-0-387-90431-3Published: 06 August 1979

  • eBook ISBN: 978-1-4612-9984-4Published: 18 December 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XXXIV, 935

  • Topics: Analysis, Difference and Functional Equations

Keywords

Publish with us

Policies and ethics

Back to top