Re: Cantor Confusion

In article <1178723452.432944.32310@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> WM <mueckenh@xxxxxxxxxxxxxxxxx> writes:
On 9 Mai, 15:50, "*** T. Winter" <***.Win...@xxxxxx> wrote:
....
But that is not the definition, their formal definition is:
"A binary relation F is called a function (or mapping, correspondence), if
aFb_1 and aFb_2 imply b_1 = b_2 for any a, b_1, and b_2."

And how do you think the a's and b's are selected? And from what sets
do you think are they selected?

The first thing you should do is find how they define "binary relation".
But if you skip introductory material you can be lead to errors.

And why do you think H&J give that informal
statement? Just in order to confuse the students?

I would not know. But to guess, to guide students? It is fairly standard
in mathematics text books to give an informal introduction to concepts so
that they can relate it to things they know.

It is ridiculous to
follow this discussion. I can assure you, if one of my students would
not know that a function is a formula (or rule or whatever) together
with a domain where it is defined and a range, then he or she would
not pass the exame. And this is the same in the better math courses in
Germany.

If that is true, it tells us a lot about mathematics education in Germany.
Functions in set theory are *not* the same as functions in analysis.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
.

Quantcast