Particularly for atheists and agnostics, mathematics and science is their god. One of the lies of physics/mathematics that gives science a mystical feel to it, is the lie that the "infinite" exists in nature. They imply that by teaching that space can be infinitely divided. They also present the absurdity that the basic "point" in geometry has no size, but when put side-by-side will add to a distance. They keep this up, giving the feel that there is an unlimited world at our fingertips. This charade is probably the result of an unintentional bias caused by the fact that man has a spiritual soul and needs the infinite....the "infinite" is only an attribute of God, not the material world. The truth is, there is a smallest possible size, which entails that "analog" does not exist in nature. I believe it was Max Planck who started to get rid of the infinite from mathematics. Wikipedia makes this comment about Planck units: "Planck units may sometimes be semi-humorously referred to by physicists as "God's units"."

We can all do an easy and instant experiment at home which proves with metaphysical certitude that space cannot be infinitely divided, even though mathematics hypothetically shows that numbers can.

This can be viewed as another version of Zeno's Paradox, the physical version of it. Aristotle dealt with the Arrow Paradox, a variant of Zeno's Paradox: "If you throw an arrow, since it is motionless in any instant, it never moves". The paradox is solved by Aristotle and Saint Thomas Aquinas who both commented that time is not made up of instants and magnitude is not made up of points. (Physica, Lib VI, Pars 9; Commentaria in Physica, Lib VI, 861.) Actually, a line is an infinite set of points,

Or think in this way. If points have dimension, then (1) either if there is no other coordinate within a point, then if you put it on a line (so that it can represent a number), there must be some numbers cannot be found on that line, and this applies to plane, cube, etc (2) or if it encompasses a range of coordinates, then you can infinitely apply the same principle to all coordinates as "starting points" and then you will get sets of coordinates after sets of coordinates.

For your objection/assertion that space cannot be infinitely divided, I am not sure what to say. But a line, plane, cube, etc are abstract, mathematical objects, with their locations represented by numbers in the form of coordinates, and they are not physical. For two points A and B on line CD, as long as they are not geometrically identical, there always exists a positive real number E is such that |A-B|>E, until they become one, identical point. And I believe this applies to physical space.

For infinity, you have to sub-distinguish. There is partial infinity (partially infinite) and absolute infinity (absolutely infinite). God has the attribute of absolute infinity, and only He has such attribute. However, other objects can have partial infinity. For instance, our souls have infinity of duration/time, for the souls are immortal. Similarly, space or universe can also be infinite, for it is within God and God is infinite regarding externality (though I am not sure if space is/can be infinite, since I have no advanced Physics training).

I am aware of Zeno.

If speculation (a theory) is disproved by demonstration, then it is not longer a theory but a falsity.

At the drop of a hat, literally, it is proven that distance cannot be infinitely divided.

There comes a point where there is "the smallest unit of distance" and it cannot be divided. Reality is digital, not analog. Think of the pixels that comprise a computer monitor. Motion appears smooth (analog) but it is actually digital.

This means that a "point" must have the smallest possible size. It is absurd to say that a point has no size (zero) and then to proceed to claim that 0+0+0+0+0+0+0+0 can equal something other than zero.

This also entails that the value of pi, while so-called "irrational" speculatively, is in reality a rational value, because there is no such thing as infinitely small beyond the decimal point. Reality is nothing but RATIONAL.

First of all, both Aristotle and Aquinas believed in the notions of motions and points. They all refuted the Zeno's Paradox and its variants by clarifying that motions do not make up time and points do not make up magnitude, nor do modern scientists say this. What you really did not get is what the lines, planes, surfaces, etc are. They are not the ways of counting points; they are ways of counting the size of a relative unit. For example, you assign a certain length as one unit, then you find a line to have the length of five units. It has nothing to do with counting the points. The points on the line are measures of position.

The dropping hat problem can be explained by the answers to Arrow Paradox (unless I understood in some different ways you intended, since you did not specify what you were specifically talking about on this) which I have already mentioned before.

Also, rational or irrational has nothing to do with your so-called "reality". It is about whether you can express a number in the form of p/q, with p and q being integers. If you can find such an expression, it is rational. Otherwise, it is irrational.

I see people get confused when dealing with speculation vs. reality. It's a problem.

Numbers are purely speculative unless you assign units to them. Numbers by themselves are worth nothing other than for mental exercise UNTIL they are assigned units that reflect something in the physical, three-dimensional created world. Speculatively the useless number equations can be termed "irrational", but when applied to the real world, they won't be, because God created a world that is only rational.

It's an irrational thing to claim a point has no size (zero), even if you say it is a "position", because once you say "next to" it would mean distance. Zero + zero, no matter how many times you put them next to each other, will always be zero....not a line. A point in geometry should be defined as the smallest possible value of distance. If you want to say a point could be the space between two pixels on a monitor, you still have to contend with the smallest possible distance between them - the pixel itself.

Dropping a hat is not a problem. It's dropped and reaches the floor because distance cannot be infinitely divided even though speculatively it does. Reality trumps theory, and makes the theory false.

Right, not only numbers are speculative, lines, spaces, etc are all speculative in mathematics. (And again, I would not talk too much on Physics, since I have no such training.) And no, numbers do not really need physical "manifestations". In Abstract Algebra, for instance, numbers are assigned to no physical meanings. (But yeah, "Abstract Algebra etc are all speculative", so "I win"!)

It is absurd to assert distance cannot be infinitely divided. As long as two points are not geometrically identical, there are space between them, and we can cut through the middle. Your failure is to make a distinction of motion/magnitude vs locomotion/point, a distinction which Aristotle and Aquinas observed, and had no problem with.

Ah, that zero+zero thing. If you are trying to figure out the distance, you have to use one coordinate to minus another coordinate, not to add their magnitude. Pixel can get infinitely smaller and smaller, but most importantly, Pixel has nothing to do with this abstract concept. "Point having no dimension" and "distance being able to be infinitely divided" do not contradict but compliment each other.

Reality does not trump theory, when you are too emphasized/influenced by intuitionism on something which is speculative in itself, and your perception on reality could be false if you failed to distinguish and sub-distinguish the differences between vital concepts.