1
Introduction
2 The Beginnings Of Zero
A Very Brief History of Zero
The Babylonian Placeholder
Other Uses of Zero as a Placeholder
Indian Mathematicians
Brahmagupta
Cantor, Infinity and Set Theory
3 The Different Types of
Zero
Placeholders, Ordinals and Quantities
Zero and the Number Line
"Nothing" versus "Number Zero"
Is Zero A Number?
What Difference Does It Make?
Useful Definitions
4 Limits and Scope
The Scope Of Equations
Scope and Rotations
5 Zero and Mathematics
Rules for Ordinals and Quantities
The Infinities
Division By Zero In Mathematics
Is Division By Zero Impossible?
0 Divided By 0
Does 1 = 2?
Reciprocals
The Riemann Sphere
Zero Raised to the 0th Power
6 Zero and Geometry
Points, Lines, Planes and Cubes
The Problem with Points
Points in a Line
Division By Zero In Geometry
Dividing a Line into Points
The Scope of Slope
7 Zero and Physics
Mathematics versus Physics
Infinities in Physics
Removing the Spurious Infinities
Division by Zero in Physics
Planck's Constant
Completeness and Incompleteness
Assignment of Results
Density of Electric Current
Density of Mass
The Lorentz Factor
Point Particles
Something into Nothing
Singularities, Black Holes and the Big Bang
Space and Time
String Theory
Renormalization
8 Zero and Computer
Software
Zero and Nothing In Software
Division by Zero in Computer Software
Issues of Scope in Computing
Endless Loops and Counting to Infinity
9 The Cult of Zero
Hearts and Minds
10 Conclusion
Changing Paradigms
Index