# uncountability

Published articles for uncountability.

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## Methods of Proof -- Diagonalization

DevFeed: [Methods of Proof -- Diagonalization](<https://devfeed.tech/articles/methods-of-proof-diagonalization-40384.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2015/06/08/methods-of-proof-diagonalization/>)

Published: 2015-06-08T09:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Collections](<https://devfeed.tech/topics/collections.md>)

Tags: [bijections](<https://devfeed.tech/tags/bijections.md>), [cardinality](<https://devfeed.tech/tags/cardinality.md>), [diagonalization](<https://devfeed.tech/tags/diagonalization.md>), [halting-problem](<https://devfeed.tech/tags/halting-problem.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [methods-of-proof](<https://devfeed.tech/tags/methods-of-proof.md>), [turing-machines](<https://devfeed.tech/tags/turing-machines.md>), [uncountability](<https://devfeed.tech/tags/uncountability.md>)

### AI overview

This tutorial introduces diagonalization as an advanced method of mathematical proof. It explains the table-and-diagonal construction and presents the theorem that no bijection exists between the natural numbers and the real numbers.

### Source excerpt

A while back we featured a post about why learning mathematics can be hard for programmers, and I claimed a major issue was not understanding the basic methods of proof (the lingua franca between intuition and rigorous mathematics). I boiled these down to the "basic four," direct implication, contrapositive, contradiction, and induction. But in mathematics there is an ever growing supply of proof methods. There are books written about the "probabilistic method," and I recently went to a lecture where the "linear algebra method" was displayed.