>>12002248>The long line is the closure of the unbounded 1D open interval.no its not, the real line is the closure of itself, not the long line
>Since the unbounded 1D open interval is not clopenBut you just said thats the real line? the real line is clopen
>It's an interval of pointswhich points?
why do you think you can define a set by calling it open?
it needs to be defined before you can put a topology on it you retard
you assumed a topology on it, IN its definition
>A point is an idea whose existence mathematicians concedethats not what it means
a point is a primitive notion of geometry, yes
a point is not primitive in the rest of math, however
there is a definition of a point in math, an element of R^n
the only primitive notion in math is the epsilon of set theory
calling a point a primitive notion is just a matter of historical respect to the ancient geometers
its like how the group axioms are called axioms, theyre not, but it was initially studied as if they were axioms
>I have assigned the definition in the other direction.youve not defined jack shit, you wrote a name for something and never explicitly wrote out what it meant
ie you gave it a name but not a definition
if you do ever try to give it a definition you dont show that it's well defined
or else you use something else thats undefined
