# 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: