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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 - mathnet@math.toronto.edu
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