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).
|Date of creation||2013-03-22 13:55:35|
|Last modified on||2013-03-22 13:55:35|
|Last modified by||matte (1858)|