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Classic Fallacies

Our mathematical correspondent has just announced some startling discoveries, claiming to have found conclusive proof that 1 is equal to 2, that every person in Canada is the same age, that a ladder will fall infinitely fast if you pull on it, and many other results that threaten the very fabric of common sense.

Of course, you know these things cannot be true. And yet, our correspondent has come up with some quite convincing "proofs" of these facts. Can you discover what is wrong with each of them?

1=2: A Proof using Beginning Algebra.
(This one is an oldie; the flaw is quite easy to spot.)

1=2: A Proof using Complex Numbers.
(This one is slightly more subtle).

All People in Canada are the Same Age.
(Finding the flaw in this one will really test your understanding of how mathematical induction works!)

A Ladder Will Fall Infinitely Fast when Pulled.
(Requires some knowledge of calculus).

Every Natural Number can be Unambiguously Described in Fourteen Words or Less.
(The flaw in this one is extremely subtle!)

Also available: a printed version of this material suitable for use as a classroom module. Contains hints on classroom presentation, each fallacious proof, and a summary of the source of the fallacy. Does not contain the individual critiques of each step that are in the interactive online version; there just didn't seem to be any appropriate way to fit them into a printed document.

Following the above link will enable you to retrieve a PostScript version of this material. You must have a PostScript printer in order to be able to print it.

This page last updated: May 26, 1998
Original Web Site Creator / Mathematical Content Developer: Philip Spencer
Current Network Coordinator and Contact Person: Joel Chan -

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