sci.math Google Group

Re: 'When Are Relations Neither True Nor False?

2010-03-20T23:28:47Z

For clarification, and for the record, I've never rejected the purely
(finite) syntactical reasoning via formal systems and Hilbert-style
rules of inference seen in Shoenfield's "Mathematical Logic" or other
_textbooks_. It's your side dubious subjective belief that one would
fully know the natural numbers to make it foundational that I'm

Re: QUESTION: how are the 4 dimensions actually used in physics math?

2010-03-20T23:28:19Z

JJ wrote:
Special Relativity
General Relativity
particle physics' collisions.
[link]
<[link]>
<[link]>
Relativity in the GPS system
<[link]>

Re: 'When Are Relations Neither True Nor False?

2010-03-20T23:25:21Z

Not quite.
A relation could be said that it is unknown whether it is
empty or not if, in defining it, it's impossible to know
whether it's empty or not. However it's still one or the
other.
Marshall

Re: aquarium fillers

2010-03-20T23:20:49Z

Virtually any artsy/craftsy store is going to have the same melted
marbles, maybe not for the same price, but once you figure in the
shipping, it'd probably be a wash. Several years ago I saw a tv news
story about a campaign in some city to reduce the use of water in
toilets by providing each household with two bricks for each toilet.

Re: Partial differential equation trivial question...

2010-03-20T23:15:27Z

How can one assume exp(z) = 1 only when z = i*2*pi*n ??

aquarium fillers

2010-03-20T22:48:46Z

I'm building an aquarium / mineral oil computer, such as
[link] . My goal is to make it
silent, as it's going in my bedroom (it'll be an mp3 (etc) player).
Looking cool is a bonus, but this will probably live inside a closed
stereo cabinet; it's not as if it'll be on display. I've got the

Re: 'When Are Relations Neither True Nor False?

2010-03-20T23:07:22Z

Technically speaking, what you said isn't quite true. A false
relation is an empty set, while a true one isn't an empty set.
A relation - a set - could be said to be neither true nor false
if in defining it, it's impossible to know whether or not it's
an empty set. For example, if you define a relation R such that

p-adic analysis and Cauchy-Riemann

2010-03-20T23:02:00Z

The p-adic numbers Qp don't have a square root of -1, if p=3 mod 4.
So would differentiable functions from Qp[i] -> Qp[i] satisfy the
Cauchy-Riemann equations? I don't know why not.
To what extent would analysis in Qp[i] have the familiar complex analysis
theorems??? You couldn't prove that Qp[i] is algebraically complete, I

Re: 'When Are Relations Neither True Nor False?

2010-03-20T23:01:14Z

There is a technical definition of truth in a model. I'm sure you
know that.
I reject that because your "belief" in the natural number is just
that and doesn't conform with your own side's technical definition
of truth in model.
Did you happen to heear hear me mentioning something like G2IT
(Godel-Goldbach Incompleteness Theorem of Knowledge) in other

Re: QUESTION: how are the 4 dimensions actually used in physics math?

2010-03-20T22:47:24Z

Time slows down while filling the curve of space in gravity.
Mitch Raemsch

Re: QUESTION: how are the 4 dimensions actually used in physics math?

2010-03-20T22:39:30Z

============
Does that violate causality ? :-)
<< the four-dimensional space-time continuum of the
theory of relativity, in its most essential formal
properties, shows a pronounced relationship to the
three-dimensional continuum of Euclidean geometrical space.
In order to give due prominence to this relationship,

Re: Partial differential equation trivial question...

2010-03-20T22:39:04Z

exp(x) = 1 implies x is on the unit circle in the complex plane. This is a
property of the exponential which you should have learned back in calculus
or even precal.
It is not difficult to prove that
exp(z) = cos(Re(z)) + I*sin(Im(z))
so when we have exp(z) = 1 we have
cos(Re(z)) + I*sin(Im(z)) = 1 = 1 + I*0

Re: Partial differential equation trivial question...

2010-03-20T22:35:45Z

But then where does all the other bits come from like n, pi, 2....
please elaborate..
Thanks

Re: p-adic analysis and Cauchy-Riemann

2010-03-20T22:27:03Z

In article <20100320204151.21D6B393...@gr ex.org>, Graven Water
Define "differentiable" ... Tell how to work with your notion.
In fact, there are non-constant functions f : Qp -> Qp that have
derivative zero everywhere.
There are non-constant bounded functions differentiable everywhere,
too. Define f(z) = 0 if |z|<1 and f(z)=1 if |z|>=1 . That's

Re: Partial differential equation trivial question...

2010-03-20T22:22:22Z

In article
<fdd1df6e-98f8-40c4-b10f-d4c0e 4da5...@q23g2000yqd.googlegrou ps.com>,
Complex numbers z with exp(z)=1 are the numbers z on your
right-hand-side. The only real number z with exp(z)=1 is
z=0.