Clegg B. Introducing Infinity: A Graphic Guide

Icon Books, 2013. — 176 p. — ISBN13: 9781848314061, ISBN: 184831406XA brand new graphic guide from Brian Clegg, author of the best-selling Inflight Science, Introducing Infinity will teach you all you need to know about this big idea, from mathematicians driven mad by transfinite numbers to the ancient Greeks who drowned the man that discovered an endless number.Big numbers
Googoled
Symbols from India
The Book of Calculation
0, a powerful tool
Archimedes: The Sand Reckoner
The poetry of infinity
Number sequences
Strange sequences
The infinity machine
Zeno’s paradoxes
Achilles and the tortoise
Apeiron
Aristotle
Potential infinity
Left brain/right brain
The power of algebra
Visual thinking
Pythagorean perfection
Diagonals of a square
Drowning by numbers
Squaring the circle
Transcendental pi
Infinity of pi
Omega
Not really numbers at all?
God and the infinite
The human perspective
“Only a manner of speaking”
Galileo
Infinity on wheels
Back to geometry
The normal rules don’t apply
The infinity of 1?
A common error
The indivisibles
Newton and potential infinity
Fluxions
From o to 0
Leibniz’s calculus
Newton vs. Leibniz
Notation
Differential and integral calculus
Battling Bishop Berkeley
The infidel mathematician
Dividing zero by zero
Flow and change
Tending towards zero
Finding a symbol
The Möbius strip and Klein bottle
Bolzano and real infinity
Cantor: mind-bending infinity
The joy of sets
Venn diagrams
Boolean algebra
Making sets of the world
Peano and the cardinals
Russell’s paradox
Cantor and subsets
Imaginary numbers
Aleph null
Cardinals and ordinals
Ordinal infinity
Countably infinite
Cantor’s elegant proof
Covering the number line
Another Cantor proof
Points in space
The shock of the infinite
Power sets
Cantor under attack
Cantor succumbs
Gödel’s shocking proof
Back to the continuum hypothesis
Does infinity exist?
Fractal infinity
Recursion
Fractals in nature
Measuring the coastline
The Cantor set
An infinite universe?
Edge of the universe?
Quantum infinity
The slit experiment
Spin
The infinitesimal
Non-standard analysis
Infinitesimals and Brownian motion
Hilbert’s Hotel
Gabriel’s Horn
The jungle of infinityFurther Reading
Author’s acknowledgements
Artist’s acknowledgements
About the Authors