Fun False Proofs

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rwald
Posts: 145
Joined: Sun Jun 13, 2004 11:43 am
Location: Caltech

Fun False Proofs

One thing that always amused me were those proofs that appeared to be true, but which had some patently untrue conclusion, such as 2 = 1. I'm curious how many such proofs people here know. I'll start off with one of the classics:

a + b = c
4a + 4b = 4c
5c = 5a + 5b
4a + 4b + 5c = 5a + 5b + 4c
4a + 4b - 4c = 5a + 5b - 5c
4(a + b - c) = 5(a + b - c)
4 = 5

The reason this one is false is fairly simple, but not all such proofs are so easy. Does anyone know some better proofs of false statements?

Tez
Posts: 29
Joined: Mon Jun 07, 2004 11:11 pm
sqrt[(x-y)]=sqrt[-(y-x)]=sqrt[-1]*sqrt[(y-x)]=i*sqrt[(y-x)]=i*sqrt[-(x-y)]=i*sqrt[-1]*sqrt[(x-y)]=i*i*sqrt[(x-y)]=-sqrt[(x-y)]

Yahweh
Posts: 446
Joined: Wed Jun 02, 2004 11:05 pm
The Laws of Physics control atoms control your brains controls YOU!
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rwald
Posts: 145
Joined: Sun Jun 13, 2004 11:43 am
Location: Caltech
Ah yes, I remember that one. Don't forget the car example...

Also, here's another more mathematically-oriented proof:

Code: Select all

x^2 = x + ... + x
x times
d/dx(x^2) = d/dx(x + ... + x)
x times
2x = 1 + ... + 1
x times
2x = x
2 = 1
For the record, I don't actually know anything. Not even this.

Ever wondered what being a Caltech undergrad was like?
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Zombified
Posts: 202
Joined: Fri Jun 04, 2004 4:37 am
Location: At a theater near you
Euler's formula:

exp(iπ) + 1 = 0

exp(iπ) = -1

(exp(iπ))^2 = (-1)^2

exp(2iπ) = 1

log exp(2iπ) = log 1

2iπ = 0

π = 0

Harry
Posts: 5
Joined: Mon Jun 07, 2004 2:48 am
Location: Cockburn
Zombified wrote:Euler's formula:

exp(iπ) + 1 = 0

exp(iπ) = -1

(exp(iπ))^2 = (-1)^2

exp(2iπ) = 1

log exp(2iπ) = log 1

2iπ = 0

π = 0
Just want to say that the symbol for pi looks bloody awful in my browser

My favourite false proof is the one that you've spent months working on. You've checked it, rechecked it and are absolutely sure that it's correct. Then some smart assed undergrad points out an obvious counter example. Seen way too many of those!
Pacifism is easy when one is masochistic

Brian the Snail
Posts: 634
Joined: Thu Jun 03, 2004 7:07 am
Tez wrote:sqrt[(x-y)]=sqrt[-(y-x)]=sqrt[-1]*sqrt[(y-x)]=i*sqrt[(y-x)]=i*sqrt[-(x-y)]=i*sqrt[-1]*sqrt[(x-y)]=i*i*sqrt[(x-y)]=-sqrt[(x-y)]
Or, sqrt[(x-y)]=sqrt[i^4]*sqrt[(x-y)]=i^2*sqrt[(x-y)]=-sqrt[(x-y)]