To exist means to have affect. Thus the substance of the universe can be aptly named "affectance". An affect is a change upon something else. Thus to exist, there must be distinction in the substance of the universe. If the universe was totally homogeneous, void of distinction, nothing could affect anything else to any more degree than it was being affected by all else and thus all would remain as it was, an infinitely vast nothingness, never actually changing at all. Nothingness and total homogeneity are the same thing.
To have infinite homogeneity or infinite similarity, there must be
infinite similarity between every point in the universe. Using a
Cartesian system, there are 3/4 * Pi * infinity^6
points in the entire universe. To have absolutely zero affectance in
the universe (zero existence) would require that all of those points be
If we assign an affectance value of X to a
point in space, every other point must be exactly equal to X. Each point
has the possibility of being anywhere from 0 to infinite in its value.
So the possibility of another point being that same X is 1/infinity.
"1/infinity" is one infinitesimal, "0+",
not zero. So the possibility of merely two points being exactly similar
still isn't zero. So at this point, we can't say that there is no
possibility of the universe being infinitely homogeneous.
If we consider another point, our possibility of all 3 of them being exactly similar is one 1/infinity times 1/infinity, or;
P = 0+^2, an infinitely smaller possibility of the 3 points being exactly similar... but still not exactly zero.
But then, the universe isn't made of merely a few points. The Cartesian model allows for 3/4 * Pi * infinity^6 points. So the possibility becomes;
P = 0+^(3/4 * Pi * infinity^6 - 1), an infinitely, unimaginably smaller possibility than before... but still not exactly zero.
far, we used the standard Cartesian model of a universe to define our
infinitesimal. But the truth is that even within the space of one
infinitesimal, there is yet another infinite number of points. So a
dimensional line would actually have, not infinity^2 points as the standard would imply, but rather infinity^3 points and 3/4 * Pi * infinity^6
points throughout. That changes our possibility considerably;
P = 0+^(3/4 * Pi * infinity^9 - 1), an infinitely, unimaginably smaller possibility than before... but still not exactly zero.
why stop at merely allowing a line to have infinity^3 points?. Why not
infinity^4 or infinity^78? The truth is that there is no limit to how
many points we can assign to a line, so lets just call it "n", yielding;
P = 0+^(3/4 * Pi * infinity^n - 1), where "n" can be anything.
But as long as n is any number, the possibility will still not be absolutely zero. And the truth is that n can be all but "absolute infinity". So, let's limit n to "the largest possible number" and call it "Largest".
Now we have the equation;
P = 0+^(3/4 * Pi * infinity^Largest - 1), as the possibility of all points being exactly similar.
And since "0+" merely means "1/infinity", we can rewrite the equation as;
P = 1/infinity^(3/4 * Pi * infinity^Largest - 1)
how can we have infinity raised to the Largest possible number without
it being larger than the Largest possible? It is an impossible number.
So what we have deduced is that in order to get the possibility of all
points in the universe having exactly similar affect value there must be
a number that is larger than the Largest possible. And there isn't one.
Thus, the possibility of all points in the universe being exactly similar is;
P = 1/(an impossibly large number) = Absolute Zero
And that is how you discover that the universe has absolutely zero possibility whatsoever of not
existing at any time. The universe could never have begun to exist
because it could never have not existed in the first place. It is a
mathematical impossibility. Nor can the universe suffer "entropy death"
or "heat death" and the thought of such is merely a mild form of terrorism.