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Infinity: A Very Short Introduction

Infinity: A Very Short Introduction  

Ian Stewart

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.001.0001
Item type: 
book
ISBN: 
9780198755234
Infinity has connections to philosophy, religion, and physics as well as mathematics. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). ... More
2. Numbers and abstraction

2. Numbers and abstraction  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0002
Item type: 
chapter
ISBN: 
9780192853615
‘Numbers and abstraction’ explains the abstract method of mathematics, which can be encapsulated in the slogan: a mathematical object is what it does, using a graph model of chess. It then ... More
Introduction

Introduction  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0001
Item type: 
chapter
ISBN: 
9780198755234
Why do we need to think about the infinite—a concept we never encounter directly? There are many reasons. Even in elementary mathematics, we encounter aspects of infinity, but more ... More
4. Eternity

4. Eternity  

Peter Adamson

in Philosophy in the Islamic World: A Very Short Introduction

Print Publication Year: 
Sep 2015
Published Online: 
Sep 2015
eISBN: 
9780191785429
DOI: 
10.1093/actrade/9780199683673.003.0005
Item type: 
chapter
ISBN: 
9780199683673
The issue most strongly associated with the history of philosophy in the Islamic world is the eternity of the universe. It features in several key works from the Islamic world—notably ... More
Philosophy in the Islamic World: A Very Short Introduction

Philosophy in the Islamic World: A Very Short Introduction  

Peter Adamson

Print Publication Year: 
Sep 2015
Published Online: 
Sep 2015
eISBN: 
9780191785429
DOI: 
10.1093/actrade/9780199683673.001.0001
Item type: 
book
ISBN: 
9780199683673
Philosophy in the Islamic World: A Very Short Introduction explores the history of philosophy among Muslims, Jews, and Christians living in Islamic lands, from its historical ... More
3. God and being

3. God and being  

Peter Adamson

in Philosophy in the Islamic World: A Very Short Introduction

Print Publication Year: 
Sep 2015
Published Online: 
Sep 2015
eISBN: 
9780191785429
DOI: 
10.1093/actrade/9780199683673.003.0004
Item type: 
chapter
ISBN: 
9780199683673
Muslims, like Jews and Christians, recognize no other divinities but the all-powerful Creator of the universe. They adhere to the fundamental belief in God’s oneness, or tawḥīd. The ... More
7. To infinity and beyond!

7. To infinity and beyond!  

Peter M. Higgins

in Numbers: A Very Short Introduction

Print Publication Year: 
Feb 2011
Published Online: 
Sep 2013
eISBN: 
9780191777820
DOI: 
10.1093/actrade/9780199584055.003.0007
Item type: 
chapter
ISBN: 
9780199584055
‘To infinity and beyond! explores the nature of infinity. Infinite sets of numbers behave differently from finite sets. Cantor proved that not all infinite sets have equally as many ... More
2. Encounters with the infinite

2. Encounters with the infinite  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0003
Item type: 
chapter
ISBN: 
9780198755234
‘Encounters with the infinite’ raises some common misconceptions about infinity, and shows how infinity naturally appears in elementary arithmetic. It aims to show how deeply embedded ... More
3. Historical views of infinity

3. Historical views of infinity  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0004
Item type: 
chapter
ISBN: 
9780198755234
‘Historical views of infinity’ focuses on historical attitudes to infinity in philosophy, religion, and mathematics, including Zeno’s famous paradoxes. Infinity is not a thing, but a ... More
5. Geometric infinity

5. Geometric infinity  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0006
Item type: 
chapter
ISBN: 
9780198755234
Much of the philosophical and mathematical fun comes from trying to tease the different meanings apart, and deciding which make sense, and why. A clear example occurs in ‘Geometric ... More
6. Physical infinity

6. Physical infinity  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0007
Item type: 
chapter
ISBN: 
9780198755234
‘Physical infinity’ moves from mathematics to the real world and tackles questions such as ‘is space infinite?’ In many areas of physics, the presence of an infinite quantity (often called ... More
3. Zeno's tortoise

3. Zeno's tortoise  

Catherine Osborne

in Presocratic Philosophy: A Very Short Introduction

Print Publication Year: 
Apr 2004
Published Online: 
Sep 2013
eISBN: 
9780191776267
DOI: 
10.1093/actrade/9780192840943.003.0004
Item type: 
chapter
ISBN: 
9780192840943
‘Zeno's tortoise’ examines Zeno's best-loved paradox, Achilles and the tortoise. Zeno's great innovation, for which he is justly famous, lies in how he persuades us to accept unwelcome ... More
Mathematics: A Very Short Introduction

Mathematics: A Very Short Introduction  

Timothy Gowers

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.001.0001
Item type: 
book
ISBN: 
9780192853615
The aim of Mathematics: A Very Short Introduction is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we ... More
4. Limits and infinity

4. Limits and infinity  

Timothy Gowers

in Mathematics: A Very Short Introduction

Print Publication Year: 
Aug 2002
Published Online: 
Sep 2013
eISBN: 
9780191776397
DOI: 
10.1093/actrade/9780192853615.003.0004
Item type: 
chapter
ISBN: 
9780192853615
In one way or another, the concept of infinity is indispensable to mathematics, and yet it is a very hard idea to make rigorous. ‘Limits and infinity’ discusses three statements that each ... More
1. How many things are there?

1. How many things are there?  

Michael Beaney

in Analytic Philosophy: A Very Short introduction

Print Publication Year: 
Nov 2017
Published Online: 
Nov 2017
eISBN: 
9780191823442
DOI: 
10.1093/actrade/9780198778028.003.0002
Item type: 
chapter
ISBN: 
9780198778028
‘How many things are there?’ introduces Gottlob Frege (1848–1925), one of the main founders of analytic philosophy whose central concern was with the nature of mathematics, and arithmetic ... More
Numbers: A Very Short Introduction

Numbers: A Very Short Introduction  

Peter M. Higgins

Print Publication Year: 
Feb 2011
Published Online: 
Sep 2013
eISBN: 
9780191777820
DOI: 
10.1093/actrade/9780199584055.001.0001
Item type: 
book
ISBN: 
9780199584055
Numbers: A very Short Introduction unravels the world of numbers; demonstrating its richness, and providing a comprehensive view of the idea of the number. This VSI paints a picture of the ... More
4. The flipside of infinity

4. The flipside of infinity  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0005
Item type: 
chapter
ISBN: 
9780198755234
‘The flipside of infinity’ examines a logical counterpart of the infinite: infinitesimals. These are quantities that are infinitely small, instead of infinitely large. Historically, such ... More
7. Counting infinity

7. Counting infinity  

Ian Stewart

in Infinity: A Very Short Introduction

Print Publication Year: 
Mar 2017
Published Online: 
Mar 2017
eISBN: 
9780191816574
DOI: 
10.1093/actrade/9780198755234.003.0008
Item type: 
chapter
ISBN: 
9780198755234
‘Counting infinity’ returns to the mathematics of infinity, discussing Cantor’s remarkable theory of how to count infinite sets, and the discovery that there are different sizes of ... More

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