Is Infinity a Number?
In short: Whether infinity behaves like a number depends on context: in calculus it can be the value of a limit but defies ordinary arithmetic, while Georg Cantor compared infinite sets by one-to-one pairing, found some larger than others, and introduced transfinite numbers.
A 1:25 short film in the series “From Fingers to Qubits”, narrated by intellect_voice_01.
Sources used in this film: Lamar University (Paul's Online Math Notes, Calculus I), “Calculus I - Limits At Infinity, Part I”; Encyclopaedia Britannica, “Georg Cantor | Biography, Contributions, Books, & Facts | Britannica”; Springer Nature (book chapter on link.springer.com), “Cantor, Finitism, and Twentieth-Century Controversies”; Encyclopedia.com, “The Independence of the Continuum Hypothesis | Encyclopedia.com”; Encyclopaedia Britannica, “Philosophy of mathematics - Logicism, Intuitionism, Formalism | Britannica”.
Sources used in this film
- Lamar University (Paul's Online Math Notes, Calculus I) — Calculus I - Limits At Infinity, Part I · View →
- Encyclopaedia Britannica — Georg Cantor | Biography, Contributions, Books, & Facts | Britannica · View →
- Springer Nature (book chapter on link.springer.com) — Cantor, Finitism, and Twentieth-Century Controversies · View →
- Encyclopedia.com — The Independence of the Continuum Hypothesis | Encyclopedia.com · View →
- Encyclopaedia Britannica — Philosophy of mathematics - Logicism, Intuitionism, Formalism | Britannica · View →
Opens the Intellect+ feed with this card first. Swipe up for the next one.
Sources
- Summary by Intellect · source: Lamar University (Paul's Online Math Notes, Calculus I): Calculus I - Limits At Infinity, Part I
- Also: Encyclopaedia Britannica: Georg Cantor | Biography, Contributions, Books, & Facts | Britannica
- Also: Springer Nature (book chapter on link.springer.com): Cantor, Finitism, and Twentieth-Century Controversies
- Also: Encyclopedia.com: The Independence of the Continuum Hypothesis | Encyclopedia.com
- Also: Encyclopaedia Britannica: Philosophy of mathematics - Logicism, Intuitionism, Formalism | Britannica
To cite this card, link to https://intellectplus.co.uk/app/is-infinity-a-number.
How we source, check and correct cards: Editorial standards.
General information, not professional advice. Spotted an error? Flag the card or see corrections and complaints.
Intellect Plus is a visual educational discovery platform for exploring fascinating facts and ideas. Brain Food, Not Brain Rot. What is Intellect Plus?
Related
More in Science · Latest · A–Z · All topics
