# toy theorem

A *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 the 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 http://planetmath.org/BrouwerFixedPointInOneDimensionthis page).

Title | toy theorem |
---|---|

Canonical name | ToyTheorem |

Date of creation | 2013-03-22 13:55:35 |

Last modified on | 2013-03-22 13:55:35 |

Owner | matte (1858) |

Last modified by | matte (1858) |

Numerical id | 7 |

Author | matte (1858) |

Entry type | Definition |

Classification | msc 00-01 |