The Definition of Points
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From: Tony Orlow on 18 Mar 2007 11:55 Virgil wrote: > In article <45fc7458(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Hero wrote: >>> On 17 Mrz., 22:13, Bob Kolker <nowh...(a)nowhere.com> wrote: >>>> Hero wrote: >>>> >>>>> So with Your kind of geometry You can or You can not tell, that DNA is >>>>> a right screw? >>>> You can tell that right and left are differnt. >>> Can You please give me a hint, where in Your geometry or in which of >>> Your geometries this is axiomized or where it follows from axioms? >>> Or where the plane-reflection is possible? >>> >>> Thanks >>> Hero >>> >>> >>> >>> >> A<B -> ~B<A >> A<B ^ B<C -> A<C > > Which is, as usual, irrelevant. > > Purely in the mathematics of three dimensional Euclidean or Cartesian > geometry, there is no way to distinguish a right handed from a left > handed system. > > I understand that there is some fairly esoteric experiment in physics > which is alleged to distinguish between them. From a mathematical point of view, it's all relative, and arbitrary, which direction is "right" or "left". It's just a matter of transitive asymmetric order relations. This applies to "less than" in the quantitiative sense, as well as "proper subset". The statements above apply to both.
From: Bob Kolker on 18 Mar 2007 11:59 Tony Orlow wrote: > > One may express them algebraically, but their truth is derived and > justified geometrically. At an intuitive level, but not at a logical level. The essentials of geometry can be developed without any geometric interpretations or references. Similarly algebraic systems (rings) can be derived from affine spaces geometry by using similar triangles to develop products from proportions. Bob Kolker
From: Tony Orlow on 18 Mar 2007 12:01 Hero wrote: > Tony Orlow wrote: >> Hero wrote: >>> Bob Kolker wrote: >>>> Hero wrote: >>>>> So with Your kind of geometry You can or You can not tell, that DNA is >>>>> a right screw? >>>> You can tell that right and left are differnt. >>> Can You please give me a hint, where in Your geometry or in which of >>> Your geometries this is axiomized or where it follows from axioms? >>> Or where the plane-reflection is possible? >>> Thanks >>> Hero >> A<B -> ~B<A >> A<B ^ B<C -> A<C >> > This is written in a math language foreign to me. > ~ means NOT > -> means Material Implication > ^ means AND > < means ? ( 3 < 4 is three is smaller than 4) > ( the only modell to Your two statements i did find: > A; B, C natural numbers, ~ means minus/negative) > > With friendly greetings > Hero > Hi Hero - '~' indeed means logical "not". '<' means "less than", and can be interpreted in a number of ways, such as "is to the left of", "is a smaller quantity than", or "is a proper subset of". You may be able to think of other examples of transitive and asymmetric relations, such as "is inferior to". :) Tony
From: Tony Orlow on 18 Mar 2007 12:07 Bob Kolker wrote: > Hero wrote: > >> Numbers are born in a huge family, the mother was time (the counting >> of days into a moon cycle, displayed as the movement of the stars of >> Nut ) and the father was space ( with features of Geb with calculi to >> count the sheep and a container to measure the grain). >> When Bob thinks, that numbers are grown up and do not need their >> father any more, that they are not about spatial objects any more, so >> why still call ,,geometry", why not call it ,,number theory"? > > Like Tevyeh in -Fiddler on the Roof- says: Tradition! > > Modern math has outgrown its parents and gone far beyond them, like any > successful Son. > > Bob Kolker > That is like saying your mind has outgrown your body, so you no longer need to eat or breathe. The language of math is the more abstract aspect, but the geometry of it is still the basis of its truth. Tony Orlow
From: SucMucPaProlij on 18 Mar 2007 12:26
"Lester Zick" <dontbother(a)nowhere.net> wrote in message news:s6tov2l53bupjlkr2fjdr82me2l8eo6q9m(a)4ax.com... > On Sat, 17 Mar 2007 12:23:28 +0100, "SucMucPaProlij" > <mrjohnpauldike2006(a)hotmail.com> wrote: > >>>>How do you define "definition"? >>> >>> Well actually this is at least several years old. I don't claim my own >>> question in that regard was necessarily original but I did raise this >>> issue at least several years ago and have routinely continued to raise >>> it. Quite possibly the silliest definition of definition I noted was >>> David Marcus's comment that a definition is only an abbreviation. >>> >> >>I think that "existence", "definition" and "number one" are equal terms. > > So what? No one cares what you think. They may or may not care what > you can prove. > >>Proof is based on a fact that you can't tell a difference between them. > > Obviously you can't. > >>I don't expect anyone to accept my proof (just as nobody takes you seriously). > > What proof? > After I've refactored my "great theory" I realized that it is just a sets theory - nothing more, nothing less. In sets theory existence, definition and "number one" are the same things. Whey you say A is element of set S then: 1) You say that A exists. 2) You say that A is defined. If A is undefined then you will say "I know that something is element of S but I can't remeber what" If A can be more that one thing then A is a set. If A is set then you must define it. If A is not defined then you can't say that A is set, right? If A can be anything then A is universal set. 3) In sets theory there can be only one A. A is unique if it exists and everything that doesn't exist is just nothing and it is not part of sets theory. I'm just chasing my tail. It is fun. Now I understand why dogs do it. |