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'toy theorem'
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| Title of object: |
toy theorem |
| Canonical Name: |
ToyTheorem |
| Type: |
Definition |
| Created on: |
2003-09-02 13:31:52 |
| Modified on: |
2004-02-17 14:40:27 |
| Classification: |
msc:00-01 |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
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\usepackage{amssymb}
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%\usepackage{psfrag}
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%\usepackage{graphicx}
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Content:
A \emph{toy theorem} is a simplified version of a more general theorem.
For instance, by introducing some simplifying assumptions in a theorem,
one obtains a toy theorem.
Usually, a toy theorem is used to illustrate the claim of a theorem.
It can also be illustrative and insightful to study proofs of
a toy theorem derived from a non-trivial theorem.
Toy theorems also have a great education value.
After presenting a theorem (with, say, a highly non-trivial proof),
one can sometimes give some assurance that the theorem
really holds, by proving a toy version of the theorem.
For instance, a toy theorem of Brouwer fixed point theorem
is obtained by restricting the dimension to one.
In this case, the Brouwer fixed point theorem follows
almost immediately from the intermediate value theorem
(see \PMlinkname{this page}{BrouwerFixedPointInOneDimension}). |
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