Sign-In
Cart
The Logic of the Infinite: Georg Cantor and the Hierarchy of Infinity
Paperback
Please select the version of book you would like to purchase.
ISBN13: 9798171938123
Publisher: Independently Published
Published: Sep 4 2026
Pages: 234
Weight: 0.70
Height: 0.49 Width: 6.00 Depth: 9.00
Language: English
Publisher: Independently Published
Published: Sep 4 2026
Pages: 234
Weight: 0.70
Height: 0.49 Width: 6.00 Depth: 9.00
Language: English
A schoolmaster's son from Saint Petersburg, stranded for life in a provincial German university where nobody important ever visited, sat down in 1873 to answer a question that had been considered improper for two thousand years. How many numbers are there? Not many. Not endlessly many. How many, exactly.
The answer Georg Cantor found broke the question in half. Some infinities, he proved, are strictly larger than others, and the proof fits on a postcard. It also fits nowhere in the mathematics of his century. Colleagues told him the work was a disease. A cardinal in Rome read his letters with more sympathy than his own department showed him. He founded the German Mathematical Society mainly because no existing society would have him, spent years arguing that Francis Bacon wrote Shakespeare, endured repeated hospitalizations, and died in a clinic in Halle during a wartime famine, three years before David Hilbert announced that nobody would drive anyone out of the paradise Cantor had built.
Boris Kriger and Anna Kriger tell that life in full, and alongside it the stranger story of what Cantor's argument turned out to be. The diagonal is not a trick for comparing sizes. It is a general-purpose machine for stepping out of any system that claims to contain everything, and once you have seen it work, you find it everywhere: in Gödel's undecidable sentence, in Turing's halting problem, in Russell's paradox, in the question of whether the physical universe has room for a single one of Cantor's infinities. Which, this book argues, it does not.
Along the way: what Aristotle actually banned and why, why a honeymoon was spent talking mathematics, how a theological argument about God's exclusivity nearly settled a question in set theory, what Kurt Gödel and Paul Cohen did to the tower of infinities, and why the hierarchy of the title is not a ladder anyone climbs.
Keywords: Georg Cantor, set theory, infinity, mathematics history, philosophy of mathematics, transfinite numbers, continuum hypothesis
Boris Kriger and Anna Kriger tell that life in full, and alongside it the stranger story of what Cantor's argument turned out to be. The diagonal is not a trick for comparing sizes. It is a general-purpose machine for stepping out of any system that claims to contain everything, and once you have seen it work, you find it everywhere: in Gödel's undecidable sentence, in Turing's halting problem, in Russell's paradox, in the question of whether the physical universe has room for a single one of Cantor's infinities. Which, this book argues, it does not.
Along the way: what Aristotle actually banned and why, why a honeymoon was spent talking mathematics, how a theological argument about God's exclusivity nearly settled a question in set theory, what Kurt Gödel and Paul Cohen did to the tower of infinities, and why the hierarchy of the title is not a ladder anyone climbs.
Keywords: Georg Cantor, set theory, infinity, mathematics history, philosophy of mathematics, transfinite numbers, continuum hypothesis
Also from
Kriger, Anna
The Brain That Lives Tomorrow: Anokhin, Experience, Predictive Processing, and the Development of Intuition
Kriger, Anna
Paperback
$13.20
Le Cerveau Qui Vit Demain: L'Expérience, Le Traitement Prédictif Et Le Développement de l'Intuition
Kriger, Anna
Paperback
$31.50
When Generosity Becomes a Wound: How Giving Too Much Can Become a Way of Asking to Be Loved
Kriger, Anna
Paperback
$15.60
Quand La Générosité Devient Une Blessure: Comment Trop Donner Peut Devenir Une Façon de Demander À Être Aimé
Kriger, Anna
Paperback
$32.77
The Crown That Keeps Us Deaf and Blind: Why We Don't Need to Humanize Animals - We Need to Humanize Ourselves
Kriger, Anna
Paperback
$21.60
Also in
Biographies General
Bluesland: Portraits of Thirteen Major American Blues Masters
Pete Welding (ED.)
Toby Byron (ED.)
Hardcover
$11.99
Karl Popper - The Formative Years, 1902 1945: Politics and Philosophy in Interwar Vienna
Hacohen, Malachi Haim
Hardcover
$236.28
Too Much and Never Enough: How My Family Created the World's Most Dangerous Man
Trump, Mary L.
Hardcover
$9.99
The Children of Athena: Greek Intellectuals in the Age of Rome: 150 Bc0-400 AD
Freeman, Charles
Hardcover
$30.40
Make It a Double: From Wretched to Wondrous: Tales of One Woman's Lifelong Discovery of Whisky
Sackier, Shelley
Hardcover
From $12.99
The Code Breaker: Jennifer Doudna, Gene Editing, and the Future of the Human Race
Isaacson, Walter
Hardcover
$12.99
Agents of Chaos: Thomas King Forçade, High Times, and the Paranoid End of the 1970s
Howe, Sean
Hardcover
From $12.99
An Enemy Such as This: Larry Casuse and the Fight for Native Liberation in One Family on Two Continents Over Three Centuries
Correia, David
Hardcover
From $12.99
Better Living Through Birding: Notes from a Black Man in the Natural World
Cooper, Christian
Hardcover
$11.99
Florence Kelley and the Nation's Work: The Rise of Womens Political Culture, 1830-1900
Sklar, Kathryn Kish
Paperback
$88.50
The Secret Life of the Savoy: Glamour and Intrigue at the World's Most Famous Hotel
Williams, Olivia
Paperback
$17.05
The Devil's Diary: Alfred Rosenberg and the Stolen Secrets of the Third Reich
Kinney, David
Wittman, Robert K.
Paperback
From $10.99
The Badger: The Life of Bernard Hinault and the Legacy of French Cycling
Fotheringham, William
Paperback
$20.89
Living with a Wild God: A Nonbeliever's Search for the Truth about Everything
Ehrenreich, Barbara
Paperback
$9.99
The Butcher, the Embezzler, and the Fall Guy: A Family Memoir of Scandal and Greed in the Meat Industry
Cherington, Gretchen
Paperback
$17.05
My Own Devices: True Stories from the Road on Music, Science, and Senseless Love
Dessa Wander
Hardcover
$9.99
How to Be Okay When Nothing Is Okay: Tips and Tricks That Kept Me Alive, Happy, and Creative in Spite of Myself
Lawson, Jenny
Hardcover
From $19.99
Nobody's Girl: A Memoir of Surviving Abuse and Fighting for Justice
Giuffre, Virginia Roberts
Hardcover
$31.50
A Walk in the Park: The True Story of a Spectacular Misadventure in the Grand Canyon
Fedarko, Kevin
Paperback
$19.80
Catch the Devil: A True Story of Murder, Deception, and Injustice on the Gulf Coast
Colloff, Pamela
Hardcover
$28.80
Dangerous, Dirty, Violent, and Young: A Fugitive Family in the Revolutionary Underground
Dohrn, Zayd Ayers
Hardcover
From $19.99