The smallest ℝeal number in Mathematics and Αlpha and Ωmega

The smallest number in mathematics is invisible to science, but geometrically looks like Jesus Christ's two Greek-letters "Alpha" and "Omega".

contents
Defining 1/infinity	Appreciating Α Ω	Takeaway summary
What Jesus said	The effect of What Jesus said

Calculus uses a special number δx = 1 ÷ infinity which is the smallest number imaginable.
It is 0.0000…00001. if 1÷10 = 0.1 and 1/100 = 0.01 then 1/infinity = 0.0000000000…001 .
“dx” is shorthand for the Greek letter Delta x = Δx or δx , because delta "Δ" is used in mathematics to mean ‘change in’ .
δX is spoken as "d X"

Revelation John Greets the Seven Churches
4John to the seven churches which are in Asia: Grace be unto you, and peace, from him which is, and which was, and which is to come; and from the seven Spirits which are before his throne; 5And from Jesus Christ, who is the faithful witness, and the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and washed us from our sins in his own blood, 6And hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen. 7Behold, he cometh with clouds; and every eye shall see him, and they also which pierced him: and all kindreds of the earth shall wail because of him. Even so, Amen.
8 I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty.

Christianity and Alpha and Omega

Because Lord Jesus after his resurrection, called himself "Alpha and Omega" the "Beginning and the ending", Christians have carefully used the ancient Greek alphabet. Because the international language during the first century was Greek, we desperately need to read the Greek Holy Scriptures to get past all the crap cultural hubris or male-dominated european culture which invades and permeates the Holy Scriptures of the God of liberty, who created man and woman equally, in fairness and love.
But here, the shapes of the letters, Alpha and Omega, the very glyphs are of interest, and I show that graphically they represent the geometric representation of *1/infinity) which is a universal truth, and the very first number countable above zero is 1/infinity, and the very last (biggest) number would be a multiple of 1/infinity, such as infinity + (1/infinity).

Defining δx = 1 ÷ infinity

"δX" exists as a ℝ Real rational number even if in Algebra infinity is undefined explicitly. (The keyword here is "defined", since variables define a single number for each evaluation of an equation. 0 < x < 3 means that x = 1 ;x = 1.1; x = 2; x = 2.9; ).
Because Infinity is a concept of the largest number imaginable that at any time (of evaluation) can be redefined as an even more larger number (infinity = infinity + 1) so that "infinity" is always increasing then (1 ÷ infinity) is always decreasing.
So δx is difficult to use honestly or visualize because its value is defined by infinity and infinity is a conceptual-value not an actual value. . But 1/infinity is a number above zero.
Infinity can be defined by an algebraic variable (X = X + 1) as X approaches infinity. X ⧴ ∞ Thus as X ⧴ ∞ then δX = 1 ÷ X. (To speak this aloud : "As X approaches infinity then delta X equals 1 divided by X.)

Calculus defines Integration of any function f(x) as [m,n]∫f(x)δX = f(x) * δx [ for all the dx within m < x < n]. And Integration is the reversal of Differentiation.
Calculus defines Differentiation of any function f(x) as: ∂f(x)/∂x = ( f(x + δx) – f(x)) / δx
You can look at δx from ∂f(x)/∂x by looking at ∂f(x) for any Cartesian graph y = f(x)
That is to say that since any number's value is actually represented in geometry a “1-dimensional line of value’s length” and since any straight line is the shortest length between two points , then we can use the two points used for ∂f(x) = f(x+ δx) – f(x) where one point is f(x+ δx) and the other point is f(x) to visualize δf(x).
This may seem so intuitively correct that there may be an exception. Look at ∂f(x) for f(x) = x^2 on wolframalpha.com. the value of f(x) approaches 1/infinity or 0 as X increases.

Let’s say ∂f(x)/∂x = 1 so that f(x) = x or y = x is a simple straight diagonal line for all values of x ⧴ ∞.

Then for those two points {f(x+ δx) ,f(x) } there is a distance along the x-axis of δx which is a single point that houses the gradient’s tangential line y = x*∂f(x)/∂x + C so that the gradient’s example line y=mx+c for that point sits on that point and kisses only that particular point on the line f(x).
What those two points are doing is meeting perpetually, due to infinity never being reached in the function δx = 1/infinity. The smallest possible length is a single dot (a 0-dimensional object), but when we assign a value to this smallest possible length, then we have an approximation-range between two values. Even if the range gets very small, because the function f(x) is on a ℝ real number domain, we can always magnify any range by dividing any number by 10 to produce a smaller range.

Okay, so in summary, the infinitesimal value {X ⧴ ∞; δX = 1 ÷ X; δx ⧴ 0} can be visualized as two meeting points f(x+ δx) – f(x) whose distance reduces to a single point which (since any value can be magnified ) so that the two points continue to perpetually meet, perpetually reducing in distance.

Looking at the Greek Letters Alpha { Α } and Omega { Ω } .

The glyph for Alpha is two lines that meet at the top. There is obviously an angle between the two meeting lines because the two lines are not parallel and thus are triangular. In other words, there are two bottom points at y=0 and midway between the two points but at y = h there is the single top point shared by both lines.
The glyph for Omega is two bottom points connected by a circular line.
So looking at the Alpha glyph to illustrate the two points of ∂f(x) = f(x+ δx) – f(x)
the bottom points of the two lines of Alpha so that one line starts at f(x+ δx) and the other line starts at f(x) and the top point is like f(x+ ½ *(1/infinity)) .
But to understand how 1/infinity looks like Omega, we must understand the perfection of geometry’s circle. Simply the area of a circle is (Area = pi* Radius^2) and if Radius is 1 (one unit of any measurement) then the Area depends on the precision of pi .
Pi is an irrational number, because it is so perfectly definable, that at any level of precision, 10 decimal places 100 decimal places billion decimal places pi is defined.
So say you have pi = 3.142 instead of 3.1415 5* 3.142 is 15.71 but 5 * 3.1415 = 15.7075. If you were multiplying the distance of a circle 10 kilometers wide, we would be off by 25 meters.
However pi can only be as precise as the precision of δx .
So when we magnify the single dot’s length of the Alpha representation of f(x+ δx) – f(x) , the ability to magnify is as assuredly possible as a ℝ Real circle is perfectly curving.

Connecting the dots.

Thus the Omega’s circle is no accident but shows the perpetually increasing perfection of ℝ domain’s 1/infinity . Omega symbolizes zooming-in on the range above and below 1/infinity to verify it’s individually smaller components.
And Alpha symbolizes zooming-out from a range of small points to the single large point, so that a single observable unit is seen even though it can be comprised by that Real range.
Jesus is the Alpha and Omega, the beginning and the end.
why you apply the idea of Alpha being zooming out abstraction to biblical "beginning situations", and when you apply the idea of Omega being zooming in individuality to theological "ending situations", then a verse where "everyone dies" but it's only individual creatures in their own individual time that die individually. And though there are many diverse life forms we all started at nearly the same time according to in Genesis 1.
When we look at Jesus Christ, the beginning of global raceless kingdom of God-of-Israel , we call the whole universal church as "body of Christ".

Sceptical Science

In order to use δx Calculus as the idea of approaches Limits.
A limit says that as X ⧴ ∞; δX = 1 ÷ X; δx ⧴ 0, as X approaches some value then δx also approaches 0. Or in other words the limit of dx is 0 even though without the concept of limits dx is never 0.
So the limit is reached at the last operation of an expression. This is a big deal, because a variable in algebra, though it can be many different values, it can only be one value in a single evaluation of an equation. So f(x) = x + x means that f(2) = 2+ 2 but not 2+3.
In basic Algebra the denominator of a fraction can’t be zero, it is illegal in algebra to divide by zero. Thus according to calculus in differentiation δx is not 0 until it is removed from being a denominator which is the objective of simplifying of ∂f(x)/∂x .
Take f(x) = x^2 then ∂f(x)/∂x
∂f(x)/∂x == ( (x+ δx)^2 – (x)^2 ) / δx

= (x^2 + 2* δx* x + δx ^2 – x^2 ) / δx	Expand the binomial	δx ⧴ 0
= ( 2* δx* x + δx ^2) / δx	Perform (x^2 – x^2)	δx ⧴ 0
= 2x + δx	Cancel out the denominator	δx ⧴ 0
=2x	Last operation reached so limit reached	δx = 0

So if δx ⧴ 0 = 0 then ∂f(x)/∂x is illegal according to Algebra at the first step. Ignoring Algebra’s rule to not divide by 0 can cause errors such as 2 = 1.

We shouldn't miss the beauty of the forest by focusing on each tree alone, nor should we miss the beauty of each tree by looking only at the forest as a whole.

The effect of Lord Jesus calling himself "Alpha and Omega" in history:
Historians knew to respect each and every letter of the Holy Scriptures, as it was written in Greek.

The Holy Scriptures of the New Testament was originally written in Greek, because Greek was the international language which was taught to the educated people, in the first century A.D.
For instance Simon Peter hired Mark to interpret into Latin for Peter's roman congregation/audiences, and so Mark spoke Greek while Peter only spoke Hebrew-Aramaic.
Eusebius in 300A.D. recorded the stories of the names of the Gospels.

Since the days of Moses who wrote down the Pentateuch 12 times for each tribe, before he died according to Jewish history. The replication of the Holy Scriptures was very accurate. Each letter was checked.
Christians believe that Jesus Christ came to fulfill every word of the Holy Scriptures because Jesus Christ is "the word" before the world was made, and the "word" became incarnated flesh who is Jesus Christ.
Yes, Christians for thousands of years have literally believed that the Holy Bible and Jesus Christ are the incarnation of the same 'the word" (which is true i've seen the holy bible be alive in my hands, once when i was getting persecuted... in 17 sept 2005 during )< br> This is why Christians always pray "praise to Christ the word" after reading holy scriptures.
however naughty they are, they knew to respect each and every letter of the Holy Scriptures, as it was written in Greek.
John was the youngest Disciple of the 12 during the life of Jesus from 1A.D. to 34A.D. we can't say he was born before 14A.D. since he was present with the women and children at the cross of Jesus, and then John was the fastest runner to the empty tomb on resurrection sunday. a sign that John was young and fast.
So Eusebius, recorded that John wrote his "Gospel of St. John", after reading the 3 other Gospels and wanting to correct the timing of the temple cleansing. Nowadays skeptical atheist biblical scholars dispute when the various scriptures were written (they follow the snake in Genesis 3 asking the question and answering with the antithesis)
But John wanted to correct and keep correct the truth of the biographies of Jesus Christ, so that we Christians in subsequent generations love him the resurrected man for who he truly was.
he succeeded in this feat

endless hope in Jesus

also we see that Christians found great hope in the endlessness of all things, where there is an end, there is the biggening, there there is new buds growing there is pruning of the old.