Can the real number line from 0 to infinity, which of course is often represented as a horizontal straight line, also be represented as being bent ninety degrees counter-clockwise at 1? I.e., if such a straight real number line representation is bent that way, does it remain a legitimate alternate representation of the real number line from 0 to infinity?
The reason that I ask includes the possibly pedagogically useful fact that, by doing so, lines connecting reciprocals (such as lines connecting 1/2 to 2, and 1/3 to 3, etc., which are usually not too well visually distinguished when such lines share a straight horizontal number line from 0 to infinity) can be readily distinguished when instead the unit line segment [0,1] is seen as the horizontal part of a real number line, and the rest of the real numbers from 1 to infinity are represented on the vertical part. The real numbers conisting of 0 and an infinite set of pairs of reciprocals also becomes more visually apparent, as well as some other properties.