Re: definition of parallel lines

["John S. Denker" <jsd@MONMOUTH.COM>]

"Frohne, Vickie" wrote:
> Actually, the "Parallel postulate" IS a formal mathematical definition.

A definition.  Not "the" definition.

> It is necessary to recognize that the word "definition" means something
> different to mathematicians than it means to the editors of Webster's.

How so?

The two definitions of definition seem more alike than
different to me -- and that is central to the point I've
been trying to make.

> ... axioms, postulates or definitions ...
> ... Changing one of the postulates and building another logical
> structure results in a different structure or "geometry."

Ditto for changing one of the axioms or definitions.

===========

When I'm sitting across the table from some folks who are
not ancient Greek geometers, I see no need to compel them
to use the Euclidean definition of "parallel" if they have
clearly stated another definition and wish to explore its
consequences.

Just as a general dictionary catalogs multiple definitions of
general words, math books catalog multiple definitions of
mathematical terms.

If you think mathematical definitions are unique and immutable,
tell me what is "the" definition of
 -- linear (I know of two inequivalent definitions)
 -- field (ditto)
 -- distribution (ditto)
 -- primitive polynomial (ditto)