# False Proof--All Numbers are Describable in at Most Twenty Words

DevFeed: [False Proof--All Numbers are Describable in at Most Twenty Words](<https://devfeed.tech/articles/false-proof-all-numbers-are-describable-in-at-most-twenty-words-40233.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/07/28/false-proof-twenty-word/>)

Published: 2011-07-28T16:03:27Z

Content type: article

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>), [Statement](<https://devfeed.tech/topics/statement.md>)

Tags: [computer](<https://devfeed.tech/tags/computer.md>), [false-proof](<https://devfeed.tech/tags/false-proof.md>), [kolmogorov-complexity](<https://devfeed.tech/tags/kolmogorov-complexity.md>), [language](<https://devfeed.tech/tags/language.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [program](<https://devfeed.tech/tags/program.md>), [set-theory](<https://devfeed.tech/tags/set-theory.md>), [turing-machine](<https://devfeed.tech/tags/turing-machine.md>), [well-ordering](<https://devfeed.tech/tags/well-ordering.md>)

## AI overview

The article examines a false proof claiming that every natural number can be described in fewer than twenty words. It explains that the contradiction arises from imprecise notions of description and set construction, connecting the issue to Russell's paradox and the Richard-Berry paradox.

## Source excerpt

Problem: Show that every natural number can be unambiguously described in fewer than twenty words. "Solution": Suppose to the contrary that not every natural number can be so described. Let $ S$ be the set of all natural numbers which are describable in fewer than twenty words. Consider $ R = \mathbb{N}-S$, the set of all words which cannot be described in fewer than twenty words. Since $ R$ is a subset of the natural numbers, which is well-ordered, it has a unique smallest element which we call $ r$.