There are lots of "proofs" that claim to prove something that is obviously not true, like It's important to recognize that while these "proofs" may be funny and cute, they always contain some error, and are therefore not real proofs.
Here's one from the Dr. Math archives:
And another:
Here's a proof that doesn't use division by zero:
Finally, here are extensive discussions of a number of false proofs:
Classic Fallacies
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 you can make a mistake in using math if you aren't careful enough. When 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.) [From the Dr. Math archives: 1 + 1 Doesn't Equal 2.]
More from the Dr. Math archives:
And see: "Plausibility Arguments," a thread from the Math Forum's mathteach discussion group archive.

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