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Convincingly Wrong Mathematical Proofs & Arguments

Updated: Aug 13, 2020

Mistakes are disappointing, but sometimes they can be entertaining. In this post, I will give a list of incorrect mathematical arguments, that are not that easy to notice, especially if you are in a hurry. A few of these delicately wrong arguments were given by me at some points of my life. I will not point out which ones, though :)


  1. An incorrect proof of the Baire category theorem for the set of real numbers



2. Does the central limit theorem contradict the law of the iterated logarithm?








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2 Comments


Elsa Yang
Elsa Yang
Oct 11, 2021

Hi Somabha, is it possible for us to see the answer somewhere?:)

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Amaryllis Chan
Amaryllis Chan
Feb 02, 2022
Replying to

I am not Somabha, but the first one is wrong since a Cantor set's complement can be open and dense without being R minus a countable set. I'm not quite sure where the mistake is though: maybe when they reference "adjacent pairs", this is not rigorous because some enumeration of the disjoint open intervals comprising U_n is assumed.


For the second one, I think when you pass from limsup to limit and find a subsequence, it depends on omega in the underlying probability space, whereas in the first statement the quantifiers are different: you first choose a subsequence and then something is true for almost all omegas.

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