April 7th, 2017, 06:52 AM  #1 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,134 Thanks: 88  Point Set Geometry
Points don't create geometry. Geometry creates points. 
April 7th, 2017, 08:07 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,459 Thanks: 693  
April 7th, 2017, 09:53 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,937 Thanks: 2265 Math Focus: Mainly analysis and algebra  Point is an undefined term in geometry. It derives its meaning from its usage definitions and axioms. Geometry is defined by the definitions and axioms. Neither creates the other, both are emergent from the definitions and axioms. This is how a point in Euclidean geometry can be different to a point in spherical geometry despite having the same core of definitions and axioms. Last edited by v8archie; April 7th, 2017 at 10:01 AM. 
April 7th, 2017, 03:08 PM  #4 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,134 Thanks: 88  Mathematics. Ref: Euclid, Euclidean Geometry; Descartes, Cartesian Geometry. Guess these essential things have been replaced by a math major in Political Science. EDIT I should be more tolerant. If you've never heard of Euclid or Descartes, or read a poem, I can understand your confusion. Last edited by zylo; April 7th, 2017 at 03:24 PM. 
April 7th, 2017, 03:24 PM  #5 
Senior Member Joined: Aug 2012 Posts: 1,521 Thanks: 364 
Just don't put Descartes before the horse.

April 7th, 2017, 03:37 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 6,937 Thanks: 2265 Math Focus: Mainly analysis and algebra  Debateable. You are doing your usual trick of assuming that everybody else is wrong simply because you don't understand the argument. Hint: to argue coherently you first need to understand the opposing point of view. Take time to read, learn and ask for explanations. That way you don't make yourself look stupid by claiming that your gut feeling based on a couple of minutes thought is somehow more valid than hundreds of hours of study by people who have spent years getting to know and understand the subject thouroughly. Get some humility, most people have lots to be humble about and neither you nor I are exceptions to that. 
April 7th, 2017, 04:26 PM  #7  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,459 Thanks: 693  Quote:
And I DO know poetry; my latest: There once was a pretty young lass Standing in water up to her knees This poem does not rhyme yet Wait till the tide comes in!  
April 8th, 2017, 04:44 AM  #8 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,134 Thanks: 88 
We have heard from Poets, Comedians, and Politicians. Amusing. Thanks. Now back to work. Having covered how you create points from geometry (locations {Descartes) on a line (Euclid)), how do you create geometry from points? Step 1) What is a point? Last edited by zylo; April 8th, 2017 at 04:46 AM. 
April 8th, 2017, 04:54 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,459 Thanks: 693 
From the math God: Point  from Wolfram MathWorld 
April 8th, 2017, 05:18 AM  #10  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,134 Thanks: 88  Quote:
EDIT: I still prefer "a point is a location on a line." Something has to be axiomatic, and the line seems best qualified. You can't go anywhere with a point (nothing). Nothing Set Topology. Last edited by zylo; April 8th, 2017 at 05:30 AM.  

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