The Definition of Points
in [Math]
|
Prev: Guide to presenting Lemma, Theorems and Definitions
Next: Density of the set of all zeroes of a function with givenproperties
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.
From: Lester Zick on 18 Mar 2007 12:40 On Sat, 17 Mar 2007 23:22:24 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick wrote: >> On Sat, 17 Mar 2007 03:08:34 GMT, Sam Wormley <swormley1(a)mchsi.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Fri, 16 Mar 2007 04:09:49 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Thu, 15 Mar 2007 02:37:12 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>>>> wrote: >>>>>> >>>>>>> Lester Zick wrote: >>>>>>> >>>>>>>> Look. If you have something to say responsive to my modest little >>>>>>>> essay I would hope you could abbreviate it with some kind of non >>>>>>>> circular philosophical extract running to oh maybe twenty lines or >>>>>>>> less. Obviously you think lines are made up of points. Big deal. So do >>>>>>>> most other neoplatonic mathematikers. >>>>>>>> >>>>>>>> ~v~~ >>>>>>> Hey Lester-- >>>>>>> >>>>>>> Point >>>>>>> http://mathworld.wolfram.com/Point.html >>>>>>> >>>>>>> A point 0-dimensional mathematical object, which can be specified in >>>>>>> n-dimensional space using n coordinates. Although the notion of a point >>>>>>> is intuitively rather clear, the mathematical machinery used to deal >>>>>>> with points and point-like objects can be surprisingly slippery. This >>>>>>> difficulty was encountered by none other than Euclid himself who, in >>>>>>> his Elements, gave the vague definition of a point as "that which has >>>>>>> no part." >>>>>> Not clear what your point is here, Sam. If the so called mathematical >>>>>> machinery used to deal with points is nothing but circular regressions >>>>>> then I certainly agree that machinery would really be pretty slippery. >>>>>> >>>>>> ~v~~ >>>>> Here's the point where I reside, Lester: >>>>> 15T 0444901m 4653490m 00306m NAD27 Fri Mar 16 04:09:09 UTC 2007 >>>> But is it a circular point, Sam? >>>> >>>> ~v~~ >>> No--it is a point (0-dimensional mathematical object) with located with >>> UTM easting, northing, elevation and time (UTC). >> >> Like I said a circular point. >> >> ~v~~ > > Nope a 0-dimensional mathematical object. What's the difference, Sam? ~v~~
From: Lester Zick on 18 Mar 2007 12:42
On Sat, 17 Mar 2007 23:23:43 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick wrote: >> On Sat, 17 Mar 2007 03:10:15 GMT, Sam Wormley <swormley1(a)mchsi.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Fri, 16 Mar 2007 04:13:10 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>> >>>>>> I don't agree with the notion that lines and straight lines mean the >>>>>> same thing, Sam, mainly because we're then at a loss to account for >>>>>> curves. >>>>> Geodesic >>>>> http://mathworld.wolfram.com/Geodesic.html >>>>> >>>>> "A geodesic is a locally length-minimizing curve. Equivalently, it >>>>> is a path that a particle which is not accelerating would follow. >>>>> In the plane, the geodesics are straight lines. On the sphere, the >>>>> geodesics are great circles (like the equator). The geodesics in >>>>> a space depend on the Riemannian metric, which affects the notions >>>>> of distance and acceleration". >>>> So instead of lines, straight lines, and curves, Sam, now we're >>>> discussing geodesics, straight geodesics, and curved geodesics? Pure >>>> terminological regression. Not all that much of an improvement. >>>> >>>> ~v~~ >>> locally length-minimizing curve >> >> As opposed to a universally length minimizing curve? Or as opposed to >> a locally length maximizing curve? Or as opposed to a universally >> length length maximizing curve? I have no idea what this is in aid of. >> Terminological regressions are a dime a dozen. In the biz they're >> called buzz words. Happy to use "geodesic" instead of "line" if that's >> all that's bothering you. There's nothing especially geo- about them. >> >> ~v~~ > > Geo is just historical baggage... Helio... etc. Sure. In which case we might just as well call them lines. ~v~~ |