Finiteness and infinity do not contradict.
Take the line for example.
***Ideally this would be best observed with pictoral examples, but words will suffice...I hope...
1. It observes a finite degree of one, where the line as infinitely projecting observes 1 as continuous.
2. The line as projective, cannot project unless there is somewhere for it to project too or from, hence the line must invert if it is to project anywhere. This inversion so to speaking observes the line going in an opposite direction from the beginning point. This is considering the point the line projects towards is the same point it is projecting from as all 0d points are the same.
3. This leads to two infinities considering the line is infinite. So now the line as multiple relative lines, through the inversion of 0d point space, is now finite yet stemming from the same infinite source. Finiteness is multiple infinities in these respects and now we have a premise for infinity to be quantified.
4. These two lines are simultaneously half of the original line. So with the inversion of the line, which for definition's sake I will call "folding", comes simultaneously quantitative expansion (multiplication) and contraction (division as fractals). This line as two lines, still however is one line considering the line is an infinite numbers of points between polar points. Hence, we can observe 3 lines in one.
5. These two lines, stemming from 3 points (one at each polarity and one in center), must continually project past there origins if they are to maintain themselves. However both lines are projecting from an origin of the center point, hence what we observe through the line is strictly the point as void existing through direction...This is considering a line is a point directed towards a point. So with that in mind the point must project towards itself, through the line.
In these respects the points at both ends are directed towards each other as these points are directed away from the center point, while towards each other as extensions of the center point. This is considering point exists through point. These end points directed towards each other effectively multiply the line, considering the line exists as one direction where quantity is specifically directional.
This forms the first angle, with this angle "condensing", as each end point is drawn towards the other. Infinite directions, are observed, or under the terms of the degree: 90 degrees (directions) are observed as 90 directions.
6. The angle as it condenses again form itself into a line, with the angle being 1 direction in itself. Under these respects the line exists as an infinitely condensing angle. In simpler terms the line exists as an angle and the angle exists as a line where one cannot exist without the other. The angle and line are duals so to speak.
7. The angles as a line must go in an opposite direction, considering the premise of the line existing is one off continually inverting directions. So the angle expands, forms into the original triadic line and contracts in the opposite direction.
8. Considering this occurs as a rate of infinity we can observe 4 directions at once (as 6 lines, vertices and horizon are 3 in 1.), through infinite grades of direction or 360 degrees, results in right/left and up/down. So now the line exists as a four directional structure as two dimensions.
9. This structure in turn must project away from its origins where the end points are directed towards each other and the center projects. This results in depth as the object goes forwards and backwards. From one angle this would appear as all lines contracting to a center point than expanding causing the object to seemingly disappear into a point and then expand from a point (or coming and going out of nothingness as it alternates between the dimensions of forwards and backwords).
This folding into "forwards" results in 4 lines as 5 with these four lines being a quarter of the original, hence the "folding function" observes 1/4 and 4 as simultaneous. This happen dually with backwords as well. So at this step we have 3 lines of horizon, vertice and depth where the line is reduced to one sixth.
The problem occurs, considering the line is the only standard of size, the lines are only relatively smaller compared to there prior localization and hence effectively are not shrinking or expanding on there own terms considering each line is infinite.
10. So with depth included we have 6 lines through 3 as 9. Now this is occurring at a rate of infinity with each "geometric object" quite literally being its own time zone. This process occurs further, and would need actual graphs at this point, until you reach infinity as a sphere with the sphere as infinite directions being conducive to 1 in itself.
11. The sphere, relativistivally, becomes a point, considering it must project in one direction and the cycle continues. Hence the point is relatively a sphere and the line is composed of infinite spheres as infinite ones and zeros.
12. Going from the points it may be observed that we have a number progression so to speak, where all numbers are actually infinities. All these steps are mere localization of infintity so too speaking; hence simultaneously proves through a folding process that there are possibility infinite ways to result in a number line.
I will stop here....