2D plane characterization for Euclidian space of >1 dimension

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Does the following characterization of a 2D plane hold for all Euclidian spaces of >1 dimension?



Plane: a two-dimensional continuum of points with unbounded area defined by two intersecting lines such that all of the lines it contains which are parallel to one of its defining lines intersect the other defining line




definition euclidean-geometry foundations plane-geometry




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  • How are you defining 'parallel' in higher dimensions than 2?
    – dbx
    Jul 23 at 13:02










  • I like equidistance and non-intersection; a nonzero distance from a point P on line m to the nearest point on line l is independent of the location of P on line m
    – bblohowiak
    Jul 24 at 16:49














up vote
0
down vote

favorite












Does the following characterization of a 2D plane hold for all Euclidian spaces of >1 dimension?



Plane: a two-dimensional continuum of points with unbounded area defined by two intersecting lines such that all of the lines it contains which are parallel to one of its defining lines intersect the other defining line




definition euclidean-geometry foundations plane-geometry




share|cite|improve this question



















  • How are you defining 'parallel' in higher dimensions than 2?
    – dbx
    Jul 23 at 13:02










  • I like equidistance and non-intersection; a nonzero distance from a point P on line m to the nearest point on line l is independent of the location of P on line m
    – bblohowiak
    Jul 24 at 16:49












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Does the following characterization of a 2D plane hold for all Euclidian spaces of >1 dimension?



Plane: a two-dimensional continuum of points with unbounded area defined by two intersecting lines such that all of the lines it contains which are parallel to one of its defining lines intersect the other defining line




definition euclidean-geometry foundations plane-geometry




share|cite|improve this question











Does the following characterization of a 2D plane hold for all Euclidian spaces of >1 dimension?



Plane: a two-dimensional continuum of points with unbounded area defined by two intersecting lines such that all of the lines it contains which are parallel to one of its defining lines intersect the other defining line





definition euclidean-geometry foundations plane-geometry





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 23 at 12:56









bblohowiak

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  • How are you defining 'parallel' in higher dimensions than 2?
    – dbx
    Jul 23 at 13:02










  • I like equidistance and non-intersection; a nonzero distance from a point P on line m to the nearest point on line l is independent of the location of P on line m
    – bblohowiak
    Jul 24 at 16:49
















  • How are you defining 'parallel' in higher dimensions than 2?
    – dbx
    Jul 23 at 13:02










  • I like equidistance and non-intersection; a nonzero distance from a point P on line m to the nearest point on line l is independent of the location of P on line m
    – bblohowiak
    Jul 24 at 16:49















How are you defining 'parallel' in higher dimensions than 2?
– dbx
Jul 23 at 13:02




How are you defining 'parallel' in higher dimensions than 2?
– dbx
Jul 23 at 13:02












I like equidistance and non-intersection; a nonzero distance from a point P on line m to the nearest point on line l is independent of the location of P on line m
– bblohowiak
Jul 24 at 16:49




I like equidistance and non-intersection; a nonzero distance from a point P on line m to the nearest point on line l is independent of the location of P on line m
– bblohowiak
Jul 24 at 16:49















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