Since this subject keeps coming up, I thought that I would polish this post up a bit to include the whole real number system and put it in its own thread.

Okay, now given that you have 10 cups with the random possibility of each cup having as many as 10 coins in it, what is the possibility that you have the same number of coins in all 10 cups?

Mathematically that would be b^10[/b] or 0.0000000001.

The state of nothingness and the state of absolute homogeneity are actually the same thing. If there is no distinction in affect at all in every point in space, there is no universe. Thus for a universe to exist, there must be distinction or variation in affect between the points in space. What is the possibility that every point in space is of the exact same value of PtA (potential-to-affect)?

Well, let’s define the term as the specific infinite series,

infA ≡ [1+1+1+…]

Just a single infinite line would give us infA^2 points on that line if you want to include all infinitesimal lengths, all “real numbers”. And assuming nothing is forcing any particular PtA value, each point on the line might have a value anywhere from infinitesimal to infinite, the range of that same infA^2 but for PtA.

So the possibility for every point on the line to have the same PtA value (given steps of 1 infinitesimal) would be;

Possibility of homogeneous line = (1/infA)^((infA)^2).

That is 1 infinitesimal reduced by itself infinitely an infinite number of times. And right there is the issue. Also in 3D space, you actually have the infinite real-number cube (to simplify from spherical) of;

Possibility of homogeneous space = (1/infA)^(infA^6)

Normally in mathematics if your number has reached 1 infinitesimal, it is accepted as zero and is certainly close enough to zero for all practical purposes but we are literally infinitely less than infinity less than 1 infinitesimal. For 3D space, we are looking at 1 infinitesimal times itself infinitely an infinite number of times, infinitely times an infinite number more times, and infinitely times an infinite number more times.

Given an infinite amount of time (an infinite timeline, another infA^2 of points in time) and with or without causality, the possibility of running across homogeneity of space is;

Possibility of homogeneity through all space = infA * (1/infA)^(infA^6)

Possibility of homogeneity through all time = (1/infA)^(infA^12)

With a possibility being that degree of infinitely small, not only can it never randomly end up homogeneous even through an infinite number of trials (an infinite time line, never getting up to even 1 infinitesimal possibility), but it can’t even be forced to be homogeneous. A force is an affect. If all affects are identical, the total affect is zero. What would be left in existence to force all points to be infinitely identical?

But if that isn’t good enough for you, realize that those calculations are based on stepped values of merely 1 infinitesimal using a standard of infA. In reality, each step would be as close to absolute zero as possible without actually being absolute zero using a standard of as close to absolute infinity as possible,

AbsInf ≡ highest possible number toward absolute infinity.

And then of course,

1/AbsInf = would be the lowest possible number or value.

Thus we have,

Possibility of homogeneity through all time = (1/AbsInf)^(Absinf^12)

Now we have truly absolute zero possibility because if we are already as close to absolute zero as possible with “1/AbsInf”, as soon as we multiply that by any fraction, we have breached absolute zero, impossibly small. And we have breached absolute zero by a factor of AbsInf^12 … well, well beyond absolute zero possibility of homogeneity.

Thus Absolute Homogeneity, “Nothingness”, is absolutely impossible.