On Sat, Nov 30, 2002 at 11:45:30PM -0500, Casey Rousseau wrote:
> OK, so I only have a B.S. in Math, so as mathematicians go, I'm pretty
> low on the hierarchy, but 1+1=2 is arithmetic, not mathematics.
> Mathematics starts when you begin exploring those things that aren't
> concrete or discrete. The Algebra, Geometry, Trigonometry and
So number theory isn't mathematics?
Number theory is usually considered the _queen_ of mathematics. (Well, for
odd values of 'usually'.) And then you have Zemelo-Frenkel set theory, which
gives modern mathematicians the tools to rigorously define and prove things
like '1+1=2'. On the 1-1 correspondence between set elements is based all of
modern mathematics.
I also checked a dictionary, which gives
That science, or class of sciences, which treats of the exact
relations existing between quantities or magnitudes, and of
the methods by which, in accordance with these relations,
quantities sought are deducible from other quantities known
or supposed; the science of spatial and quantitative
relations.
Note: Mathematics embraces three departments, namely: 1.
{Arithmetic}. 2. {Geometry}, including {Trigonometry}
and {Conic Sections}. 3. {Analysis}, in which letters
are used, including {Algebra}, {Analytical Geometry},
and {Calculus}.
> Arithmetic most of us studied up through high school simply gives you
> the tools to begin exploring Calculus, Abstract Algebra, Analysis,
> Statistics, etc.
True, but it doesn't mean the first stuff isn't mathematics. Now, the _way_
it's taught may not be much like mathematics (i.e. "here's a formula,
memorize it").
-xx- Damien X-)