Infinities in Mathematics:
For this let’s consider the number line:
a) Infinity, (∞) = {1, 2, 3, 4…}
c) Infinity, (∞) = {… -3, -2, -1, 0, 1, 2, 3 …} = {-∞…,-3, -2, -1, 0, 1, 2, 3 …, ∞}
d) Infinity, (∞) = {1, (1/2), (1/4), (1/8), (1/16), (1/32), (1/64) …}
The sets presented in (a), (
The number line consists of many infinite sets, for example the sets of natural numbers, integers, rational numbers, even numbers, and odd numbers are all infinite in size (where size represents the number of terms present in the set). However, my favorite thing about the number line is the fact that if any two numbers are chosen at random there is an infinite set of rational numbers of various sizes between them. Set (d) from above shows an example of this: it shows one of the sets of an infinite amount of rational number of various size (size indicating their relative distance from the reference point zero) present between zero and +1. That is, this infinite set is present in the range of (+1 ≥ X > 0), where X is an element in the set. Therefore, if the numbers 2 and 3 are selected and a particular rational number between them chosen to be approached but never reached a set with an infinite amount of terms would be obtained similar to the example in set (d). Thus, it can be concluded that between 0 and 1 there is at least one infinite set of rational numbers of various sizes; the same could be said for between 2 and 3, 3 and 4, 4 and 5, 1 and 5, 2 and 5, 11 and 12, 12 and 32, and so on. If this is still not clear, let’s say we have the number 1, if it is divided into 4 equal parts, each part would be a quarter with (1/4), (2/4), (3/4) and (4/4) representing the relative distance of each quarter from the zero point. If one of the four parts form above is then divided again into four equal parts and again one of these selected and divided in to four, and so on. This would result in an infinite set with zero as the asymptote; the same could be said if something or a number is continuously divided into say two, three, six or even one hundred equal parts. It should be noted that all the infinities above has the same size (that is, the same number of terms). If the same principles about infinite sets are adopted for the 3-dimensional plane of the X-axis, Y-axis and Z-axis the entire universe can be looked at in a new way.
Real infinities:
Let’s consider for a moment that we had the ability to do what ever we wanted to do, the power to do absolutely any thing. Then, let’s say we used this ability to remove the entire expanding cosmic matter web of the observable universe. The removal of all the cluster and super clusters of galaxies present in it (containing galaxies numbered in the hundreds of billions), all its dark matter, all its stars, all its super massive black holes, every organized body of matter, every unit of mass, every energy emitting body and particle, every electron, proton and neutron, every photon, every neutrino. That is, the removal of every particle that has the ability to absorb or emit any form of energy, the removal of every energy waves and particles of every size and the removal of every /any gravitational source. And let say that an innumerable amount of other universes exist alongside our and we also removed all these universes the instant ours was removed. Subsequent, an Infinite Void would be left or revealed, an infinite region of nothingness, an empty infinite region, space itself would be an infinite void/ vacuum.
This Emptiness/ Infinite Void should not be thought of in terms of when, where, how and why it exist or was created or how and when it will be destroyed, broken down or moved. It should be thought of as a single medium that has always existed and will always exist; and as a medium infinite in size with every meter, kilometer, square meter and cubic kilometer being of the same consistency and being made up of nothing; as this infinite medium would have no mass, no energy and no forces acting within it. That is, in every cubic meter of this Infinite Void only empty space would be present, and would be of the same consistency, and should not be thought of as more empty space being concentrated in one region or area compared to another.
Let’s look at it like this:
The entire Infinite Void could be looked at as consisting of an infinite amount of 1 cubic kilometer cubes, cubes the size of protons, cubes the size of atoms, cubes the size of planets, cubes the size of galaxies or cubes the size of universes made of empty space all of which are exactly alike in consistency. This emptiness could and would only be arranged in one way.
This Infinite Void could be looked at as a set which contains an infinite amount of zeros, this would be a null set and would be the same as a set containing only five zeros.
That is, Infinity, (∞) = {0, 0, 0, 0 …, 0, 0, 0, 0} = {0, 0, 0, 0, 0} = {}
Therefore, for the number of possible arrangements (0!) or zero factorial is used.
For this let’s use the set of five zeros {0, 0, 0, 0, 0} this set contains five repeating element, where all five of the element are exactly alike with no distinctions.
(0!) = N! / R! Where N is the number of terms and R is the number of repeated terms
(0!) = N! ÷ R!
(0!) = 5! / 5!
(0!) = 1
Therefore, there is only 1 way of arranging a set containing nothing or one possible arrangement for such a set. Therefore, in terms of the Infinite Void or nothingness of space being discussed, if a region of emptiness 1 cubic kilometer in size is say 1 light year away from another region of emptiness also 1 cubic kilometer in size, the first region can not be moved to replace the second one. That is the nothingness of space, which is empty or vacant of all matter, energy and forces, does not move or change; that is, in the Infinite Void, regions next to one another do not move to replace each other. Thus, it can be concluded that the entire infinite and empty medium is perfectly still or motionless (stationary or not flowing) however, even in this context time would still be moving.
The Infinite Void would have no middle point (no region in it / neither in space nor in time to call its middle); it would have no shape as it has no end points (that is, no physical or absolute point when or where this nothingness or emptiness ends in physical space or in time). Thus, there could be no traveling around the Void or traveling form one end of the Void to the next. It would only contain reference point that is one region would be a relative distance away from another region in space and also in time. That is, one region the size of earth could be said to be 1000 kilometers away from another region the size of Jupiter. These principles, above, were adopted from those which apply to infinities on the number line. Thus, within the single infinite medium called the Infinite Void, on any given side of any given region of any given size, within the Void, there is an infinite amount of other regions, infinite in number and size (that is an infinite amount of infinitely large and infinitely small regions). This not only applies to physical regions in space but it also applies to time span of the Infinite Void; as there would be an infinite amount of infinitely large and infinitely small regions or units of time on either side of any given single point or unit of time in the past, present and future. Since, one region or point in time could or would be Pico seconds, Nanoseconds, microseconds, seconds, minutes, hours, days, or even millions of billions of billions of billions of years away form another point in time, in any given direction (either in the past or in the future). The sentence that preceded this one, shows that regions or points in time are all relative to one other point in time; thus, all points in time, an infinite amount of them in the past or in the future, are relative to one point. Which is the reference point for time, and this point is exactly now, no wait it is exactly now, now, now, no wait a second, exactly now, no exactly this instant. Ok, from the illustration above it can be seen or it could be concluded that the reference point is the present (what we refer to or look at as now), and this reference point is not stationary, in fact it is motion or mobile. That is, 9 billionth of a Pico second, 2 Pico seconds, 6 Nanoseconds, 100 microseconds, 15 seconds, 3 minutes, 10 hours, 15 days, or even 6000 million billion trillion years from now will eventually become the present and will remain the present only for an instant. Since, if any point from now or from the present is consider to be in the future, it will remain or continued to be looked at as the future, until the instant it becomes the present, after which it will become the past. That is, a minute from now is looked at as the future or being in the future, at exactly one minute from now it will become the present and instantaneously changed in or become the past.
In terms of the consistency of the entire Emptiness or Void, if a region the size of a galaxy is selected and a second region the size of the space between the nucleus of an hydrogen atom and the electron in the lowest energy level (orbital/ shell) of that same hydrogen atom is selected; and the two regions compared they would be of exactly the same consistency of nothingness. Even if this second region is divided into ten parts and each of those into ten parts and each of those into ten parts, and so on in an infinite sequence or infinite amount of times, each of these infinite amounts of small regions of emptiness would be of exactly same consistency as the region the size of a galaxy.
Now that the Infinite Void or infinite region of nothingness has being carefully explained we will again use our ability, to do what ever we want, to instantaneously bring back all the matter and energy back into our universe and reorganized all this matter and energy back on or within the medium , the Infinite Void, which contains it. And in so doing bring back our cosmic matter web and all the other bubbles of universes, if any exists, that we might have move.
Now that the existence of the Infinite Void has been established, the question of the Big Bang and the creation of our universe can be brought into the equation, with a new way of looking at this entire situation. The Infinite Void would have always exist, infinite in its size and time scale, and for a very long time this medium would have contained nothing (would be absolute emptiness) but would have always had the ability to allow matter and energy to exist and organized itself within it. Now some 13 billion years ago, at the instant just before the Big Bang, this region where our universe is now currently located, would have been a part of the Infinite Void and would have contain no matter and energy of any form, size or intensity. However, in one instant at a single point (that is, at a single point in time and in space) all this would change; as from a single point all the matter and energy needed to create an entire universe would be spilled out into this particular region of the infinite medium. The particles, energy and forces from the Big Bang would be forced outwards in all directions away from this point of origination, like a rapidly expanding and very energetic bubble. Now the question could be ask was the only point in this infinite medium (the only location or region in this infinite space and in the infinite time span of the Infinite Void) where such a massive burst of energy could occur and why would this be the only location, point or region chosen for this occurrence? And derived from that question, another hypothetical question could be asked, did some 50 thousand million billion years ago in a region or at a single point some 9 hundred thousand million billion trillion light years away from our universe (or away from the point of origination of our universe) did a similar burst spill out another large quantity of energy into that particular region of the infinite medium to create another universe? For the above questions, don’t view the very large time span and distances as suspicious or speculative as when working with infinity those large values are considered to be comparatively small.