Let a statement be of the form of an implication
is the converse of the first. In other words, from the former one concludes that is necessary for , and from the latter that is necessary for .
If there is originally a statement which is a (true) theorem and if its converse also is true, then the latter can be called the converse theorem of the original one. Note that, if the converse of a true theorem “If then ” is also true, then “ iff ” is a true theorem.
For example, we know the theorem on isosceles triangles:
There is also its converse theorem:
If a triangle contains two congruent angles, then it has two congruent sides.
Both of these propositions are true, thus being theorems (see the entries angles of an isosceles triangle and determining from angles that a triangle is isosceles). But there are many (true) theorems whose converses are not true, e.g. (http://planetmath.org/Eg):
|Date of creation||2013-03-22 17:13:37|
|Last modified on||2013-03-22 17:13:37|
|Last modified by||pahio (2872)|