
remarkable how few people recognize a contradiction when shown one #35.6 Unitext 8th ed.: TRUE CALCULUS
Posted:
Nov 2, 2013 4:06 PM


On Saturday, November 2, 2013 2:41:32 PM UTC5, Wally W. wrote: > On Fri, 1 Nov 2013 14:00:29 0700 (PDT), Archimedes Plutonium wrote: > > > > >the ugly contradiction at the heart of High School Geometry #35.3 Unitext 8th ed.: TRUE CALCULUS > > > > > >On Friday, November 1, 2013 4:23:16 AM UTC5, WizardOfOz wrote: > > >> Archimedes Plutonium <plutonium.archimedes@gmail.com> wrote in > > >> > > >> news:61096865a35e48939198062222fce03e@googlegroups.com: > > >> > > > > > >> > > >> > > >> There is no empty space between the points that lie on a line in > > >> > > >> geometry. None. > > >> > > >> > > >> > > >> > > >> > > >> > So you have Point, Empty Space, > > >> > > >> > Next Point, which gives the line its length. > > >> > > >> > > >> > > >> Nope. That's not geoemtry. > > >> > > > > > >Someone said this fool of Wizard of Oz is Eric Gisse. Can someone verify? > > > > > >Now I do not write this to teach a fool for they are unteachable. > > > > > >I write this for the readers that know logic. That know a contradiction when it is pointed out. > > > > > >So you have in Old Geometry that a line is a set of points, and that points are without length, without width and without depth. But you are told a line has length. So how can a line have length if points never have length? > > > > So Zeno's arrow can't exist. It could never hold together in flight > > because it is not continuous. >
Think about your rebuttal for a minute. You cannot have a solid stick because the electrons of atoms are mostly empty space and not continuous, so a solid stick does not exist.
What you should be thinking about is that Old Fake Geometry says this:
Point  it has no length, it has no width and no depth
Line  it has length, but it has no width and no depth
And that is the full and the end of the story for point and line in Old Fake Geometry.
Any person with logic and commonsense can see through that failure and recognizes there is a main ingredient missing. That you cannot yield length from points that have no length. You need a third ingredient to give you length of a line.
That third ingredient comes forth from the fact that you have finite and infinite in Geometry and the two have a borderline between them. So you figure out what the borderline is. If it is the number 10 as in the 10 Grid then macroinfinity starts after 10 and microinfinity is the 1/10. So that means holes exist between 0 and .1 and then .1 and .2. Holes of empty space where no finite point exists.
That is how Geometry gains length for lines, be having 3 entities:
Point Empty Space Line
If you like being a stupid mathematician that lives with, accepts a contradiction in your math, then be my guest. But most people who pride themselves on being a mathematician will not live with a contradiction as their understanding of geometry.
> > > > > > > >Well that is a logical contradiction. > > > > > >The only remedy is to insert emptyspace between one point and its successor point. > > > > Define a "successor point". > >
When you have only finite points surrounded by empty space of infinity points, then you have a situation of 1st finite point, then empty space, then 2nd finite point, then empty space, then 3rd finite point then empty space until you reach macroinfinity.
AP

