A generalized form of the diagonal argument was used by Cantor to prove Cantor's theorem: for every set S, the power set of S —that is, the set of all subsets of S (here written as P (S))—cannot be in …

Jan 13, 2025 · The diagonal proof is often called Cantor’s proof, because Georg Cantor was the first person to come up with it, though the version of the Diagonal proof that you commonly see today is …

George's most famous discovery - one of many by the way - was the diagonal argument. Although George used it mostly to talk about infinity, it's proven useful for a lot of other things as well, including …

Cantor's point is that the real numbers cannot be so listed. One way to arrange the proof is to assume that such a list can be given, and derive from that a contradiction by showing that the list does not …

Cantor's Diagonal Argument Theorem: The set of real numbers in the interval $ [0,1]$ is uncountable. Proof: We will argue indirectly. Suppose $f: \mathbb {N} \rightarrow [0,1]$ is a one-to-one …

Nov 14, 2025 · However, Cantor's diagonal method is completely general and applies to any set as described below. Given any set S, consider the power set T=P (S)...

Jun 14, 2025 · Cantor's Diagonal Argument is a mathematical proof that demonstrates the set of real numbers is uncountably infinite. It involves assuming a list of all real numbers, constructing a new …

Guide to Cantor's Theorem Hi everybody! In this guide, I'd like to talk about a formal proof of Cantor's theorem, the diagonalization argument we saw in our very first lecture.

Simplicio: I'm trying to understand the significance of Cantor's diagonal proof. I find it especially confusing that the rational numbers are considered to be countable, but the real numbers are not. It …

An online English translation of Cantor’s 1891 Diagonal Proof, along with the original German text (Über eine elemtare Frage de Mannigfaltigkeitslehre).