Playing with Infinity

Popular account ranges from counting to mathematical logic and covers the many mathematical concepts that relate to infinity: graphic representation of functions; pairings and other combinations; prime numbers; logarithms and circular functions; formulas, analytical geometry; infinite lines, complex numbers, expansion in the power series; metamathematics; the undecidable problem, more.

INTRODUCTION
PART I THE SORCERER'S APPRENTICE
1 PLAYING WITH FINGERS
2 THE 'TEMPERATURE CHARTS' OF THE OPERATIONS
3 THE PARCELLING OUT OF THE INFINITE NUMBER SERIES
4 THE SORCERER'S APPRENTICE
5 VARIATIONS ON A FUNDAMENTAL THEME
    POSTSCRIPT ON GEOMETRY WITHOUT MEASUREMENTS
6 WE GO THROUGH ALL POSSIBILITIES
7 COLOURING THE GREY NUMBER SERIES
8 I HAVE THOUGHT OF A NUMBER'
PART II THE CREATIVE ROLE OF FORM
9 DIVERGING NUMBERS
10 LIMITLESS DENSITY
11 WE CATCH INFINITY AGAIN
12 THE LINE IS FILLED UP
13 THE CHARTS GET SMOOTHED OUT
14 MATHEMATICS IS ONE
    POSTSCRIPT ABOUT WAVES AND SHADOWS
15 WRITE IT DOWN' ELEMENTS
16 SOME WORKSHOP SECRETS
17 MANY SMALL MAKE A GREAT'
PART III THE SELF-CRITIQUE OF PURE REASON
18 AND STILL THERE ARE DIFFERENT KINDS OF MATHEMATICS
    POSTSCRIPT ABOUT THE FOURTH DIMENSION
19 THE BUILDING ROCKS
20 FORM BECOMES INDEPENDENT
21 AWAITING JUDGEMENT BY METAMATHEMATICS
    POSTSCRIPT ON PERCEPTION PROJECTED TO INFINITY
22 WHAT IS MATHEMATICS NOT CAPABLE OF?
  AFTER USE