Julio It is not quite that balanced a choice. There are choices (and definitions) which help you think more clearly, and which correspond to how a community of people communicate, and others which don't serve those purposes. It is not a question of proof, but of making a choice which works, and mathematicians have consistently found that the inclusive definition fits how we reason, and how we communicate.
You example is a nice illustration that the person who wrote the problem almost certainly was thinking about the inclusive definition. This is what would be used in any advanced math context, or book. The problem does NOT make explicit that it is the inclusive or exclusive definition. There are two choices - the problem came from some sensible context and the context will help you decide what definition fits. OR the problem is artificial, just made up in a text book, and you will have to check how the book uses the words. Hopefully, the book has enough mathematical quality to use the inclusive definition.
Julio Albornoz wrote:
> Hello fellow math fanatics, > > The arguments about inclusive and exclusive definitions can go on for > ever especially when one tries to make one point over another. In > reference to rectangles and squares, weather a square can be defined > as a "kind of rectangle" remains to be mathematically proven. > > However, let's take the real fact: > > Suppose a problem reads: The perimeter of a "rectangle" is 48 ft. > Using whole numbers only, what is the dimensions that would give the > greatest area? > > If we are inclusive we can say that is a 12 ft by 12 ft = 144 sq ft. > If we are exclusive we can say that is a 13 ft by 11 dt = 143 sq ft. > > But what would the "correct" answer be in the real test-answer world? > > Wouldn't you agree that since the problem stated "rectangle" the > exclusive way would be the correct answer? > > Your comments will be appreciated. > > Regards, Julio