# false proof

Published articles for false proof.

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## False Proof: 1 = 2 (with Calculus)

DevFeed: [False Proof: 1 = 2 (with Calculus)](<https://devfeed.tech/articles/false-proof-1-2-with-calculus-40245.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/10/25/false-proof-1-2-with-calculus/>)

Published: 2011-10-25T14:46:12Z

Content type: tutorial

Language: en

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

Topics: [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [function](<https://devfeed.tech/topics/function.md>), [Variable](<https://devfeed.tech/topics/variable.md>)

Tags: [calculus](<https://devfeed.tech/tags/calculus.md>), [false-proof](<https://devfeed.tech/tags/false-proof.md>), [function](<https://devfeed.tech/tags/function.md>), [logic](<https://devfeed.tech/tags/logic.md>), [variable](<https://devfeed.tech/tags/variable.md>)

### AI overview

This article presents a false calculus proof that 1 equals 2 and explains that the error comes from differentiating a variable-length sum with respect to only one of its variables.

### Source excerpt

Problem: Show 1 = 2 (with calculus) "Solution": Consider the following: $ 1^2 = 1$ $ 2^2 = 2 + 2$ $ 3^2 = 3 + 3 + 3$ $ \vdots$ $ x^2 = x + x + \dots + x$ ($ x$ times) And since this is true for all values of $ x$, we may take the derivative of both sides, and the equality remains true. In other words:

## 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$.

## False Proof--The Reals are Countable

DevFeed: [False Proof--The Reals are Countable](<https://devfeed.tech/articles/false-proof-the-reals-are-countable-40228.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/07/19/false-proof-the-reals-are-countable/>)

Published: 2011-07-19T17:10:00Z

Content type: article

Language: en

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

Topics: [math](<https://devfeed.tech/topics/math.md>)

Tags: [axiom-of-choice](<https://devfeed.tech/tags/axiom-of-choice.md>), [countability](<https://devfeed.tech/tags/countability.md>), [false-proof](<https://devfeed.tech/tags/false-proof.md>), [math](<https://devfeed.tech/tags/math.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [set-theory](<https://devfeed.tech/tags/set-theory.md>), [well-ordering](<https://devfeed.tech/tags/well-ordering.md>)

### AI overview

The article examines a purported proof that the real numbers are countable. It explains that the argument's surjectivity claim is flawed and begins demonstrating the issue using a chosen well-ordering of the integers.

### Source excerpt

It seems that false proofs are quickly becoming some of the most popular posts on Math ∩ Programming. I have been preparing exciting posts on applications of graph coloring, deck stacking, and serial killers. Unfortunately, each requires resources which exist solely on my home desktop, which is currently dismantled in California while I am on vacation in Costa Rica. Until I return from the tropics, I will continue with more of the ever -popular false proofs.