Physics Banter - View Single Post - Core error argument objection refuted, short

**Dik T. Winter**

In article (James Harris) writes:
(James Harris) wrote in message om...
"Dik T. Winter" wrote in message ...
....
Why? Please prove that.

It has to do with continuity and slope. If you could have w_1(m) and
w_1(m') equal when m does not equal m' then at that point you'd have
infinite slope or a discontinuity.

OOPS! What I said was STUPID!!!

Yes.

Oh yeah, so how do you prove that a varying function in algebraic
integers has to have an infinite number of results?

Anybody? Anybody?

The simple answer is: you can't. For instance the function (assume x an
algebraic integer):
f(x) = 2 when x/2 is an algebraic integer,
f(x) = 1 otherwise,
is a perfectly well-defined varying function in the function that has
only two possible results.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/