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

**Dik T. Winter**

In article (James Harris) writes:
"Dik T. Winter" wrote in message ...
....
The simple answer is that if w_1(m) varies with m, then it must vary
over an infinite number of algebraic integer values as m varies over
algebraic integers.

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.

Ah, you assume a continuous function. Why?

But w_1(m) must vary from 0 to infinity if it varies with m.

Why? Please prove that.

It turns out that you need the the absolute value, like r(m)r*(m), and
with it it's possible to show that for an algebraic integer function
that varies as m varies--a continuous function--as m varies over all
of algebraic integer r(m)r*(m) must vary from 0 to positive or
negative infinity.

Assuming a continuous function again. Why?

It's like saying that you can have xy=2, where x and y are integers,
or algebraic integers, where x varies over the ring, and y remains in
it, though of course, I can just show that for x=5 that doesn't work.

Not at all. The range of w_1(m) may be severely limited, while the
range of x is not limited. It is similar to saying that you can have
xy = 2, where x ranges over the algebraic integer factors of 2, and so y
also ranges over the algebraic integer factors of 2. 5 is now not
a counterexample because it is not an algebraic integer factor of 2.

Yeah you can *say* just about anything, but mathematically that
statement is bull****, and for me to have made the discoveries I've
made and be stuck because a lot of posters can get away with bull****
is just ****ing me off.

You are producing the bull****. Pray produce a proof that w_1(m) is a
continuous function and we can talk further.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/