volume_mute

How Many Kinds of Infinity Are There?

publish date: 2026/05/23 22:07:23.450725 UTC

volume_mute

Is there only one kind of infinity, or are there multiple distinct infinities?

There is only one kind of infinity, symbolised by ∞

There are exactly two: countable and uncountable

There is an infinite hierarchy of distinct infinities

Infinity is not a mathematical concept — it is only philosophical

Correct Answer

There is an infinite hierarchy of distinct infinities

Explanation

There is not one but an infinite hierarchy of distinct infinities: \(1 < 2 < 3 < \cdots < \aleph_0 < c < 2^c < 2^{2^c} < \cdots\). Each step produces a strictly larger infinity (via the power set operation). There is exactly one countable infinity (\(\aleph_0\)), and beyond it lie infinitely many uncountable infinities, all distinct from one another.

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

Quizzes you can take where this question appears

Infinity