Can somebody explain to me Cantor's diagonalization argument?
23 Every argument is an argument for something. The Cantor diagonal argument is an argument to prove that set of real numbers is uncountable. What is a countable set? A set is countable if …
elementary set theory - How does Cantor's diagonal argument …
95 I'm having trouble understanding Cantor's diagonal argument. Specifically, I do not understand how it proves that something is "uncountable". My understanding of the argument is that it …
logic - Why doesn't Cantor's diagonal argument prove only that …
Apr 10, 2025 · In this answer to the question Why are the total functions not enumerable? the following argument is made: Because of diagonalization. If $(f_e: e \\in \\mathbb{N})$ was a …
Georg Cantor's diagonal argument, what exactly does it prove?
3 For your specific questions: Georg Cantor's diagonal argument, what exactly does it prove? (This is the question in the title as of the time I write this.) It proves that the set of real numbers …
analysis - Why doesn't Cantor's diagonal argument also apply to …
In my understanding of Cantor's diagonal argument, we start by representing each of a set of real numbers as an infinite bit string. My question is: why can't we begin by representing each natural
elementary set theory - Understanding Cantor's diagonal …
Nov 23, 2015 · I'm trying to grasp Cantor's diagonal argument to understand the proof that the power set of the natural numbers is uncountable. On Wikipedia, there is the following …
elementary set theory - Cantor's diagonal argument applied to …
Nov 4, 2013 · 2 How to prove that the new number produced by the Cantor's diagonalization process applied to $\Bbb Q$ is not a rational number ? Suppose, someone claims that there is …
Improving my understanding of Cantor's Diagonal Argument
I studied Cantor's Diagonal Argument in school years ago and it's always bothered me (as I'm sure it does many others). In my head I have two counter-arguments to Cantor's Diagonal …
logic - Why doesn't Cantor's Diagonal argument depend on the …
0 This question already has answers here: What ZF axioms does Cantor's diagonal argument require? (1 answer) Do you need the Axiom of Choice to accept Cantor's Diagonal Proof? (1 …
combinatorics - Clarification about Cantor's Diagonal argument …
May 5, 2024 · Cantor's Diagonal Argument is almost always taught incorrectly, in several ways. Some are immaterial; for example, he used it on infinite-length binary strings, not real numbers.