1 + 1 Doesn't Equal 2

Date: 06/04/98 at 20:22:58
From: Sara Locker
Subject: 1 + 1 doesn't = 2

It's a proven fact that 1 + 1 does not equal 2. What is the math 
equation that proves this? My math teacher taught me this, but I 
forget.

Sara

Date: 06/06/98 at 12:55:27
From: Doctor Peterson
Subject: Re: 1 + 1 doesn't = 2

Hi, Sara. There are actually lots of "proofs" like this, so I can't 
tell which one you might have seen. Here's a classic example on the 
Web that proves 1 = 2:

  http://www.astro.virginia.edu/~eww6n/math/Fallacy.html   

And here's a "proof" that 1 + 1 = 1 in our own archives:

  http://mathforum.org/dr.math/problems/mayer9.4.97.html   

and another that 2 = 1:

  http://mathforum.org/dr.math/problems/wall10.3.97.html   

Finally, here's a good discussion of several "proofs" like this:

  http://www.math.toronto.edu/mathnet/falseProofs/   


Of course, these aren't really proofs, because they all have some 
error in them. What's important about these examples is that they show 
ways in which you can make a mistake in using math if you aren't 
careful enough. If you can understand where the error is, then you can 
look for the same kinds of errors in your own work, whether it's a 
proof for school or a calculation you make when you're designing a 
bridge. It also explains why mathematicians and scientists don't 
publish their results without first having others check them to make 
sure there isn't some subtle error in their calculations.

-Doctor Peterson,  The Math Forum