Literally, it refers to an illusory number that does not exist.
Let’s take an example.
For example, the quadratic equation x2 1=0 has a simple structure, but no solution can be found for x in the formula within the entire range of real numbers.
If you must find the solution to x, then you need to search in the field of imaginary numbers.
So, what to do?
Very simple.
First, imagine that in the endless nothingness, there is a straight line extending infinitely to the left and right without any end.
Then find, or select, a point on this straight line, define it as 0, and then define it as the origin.
Then, on the right side of this origin (0), define a point at a certain distance away, which is 1.
Next, walk a distance to the right of 1 that is exactly the same distance between 1 and 0.
Stop and define another point, which is 2.
From this, the analogy goes on indefinitely.
You can continue to push out 3, 4, 5, 6... until infinity.
Then all points on this straight line that are equidistant between 0 and 1, between 1 and 2, and between 2 and 3 are integers.
And all points between 0 and 1, between 1 and 2, and between 2 and 3 are fractions and irrational numbers.
Finally, all points to the right of the origin (0), whether irrational numbers, fractions or integers, are all positive numbers.
As for all points on the left side of the origin (0) and all points on the right side of the origin (0) that are perfectly symmetrical, they are all negative numbers.
Therefore, the numbers on this infinite straight line are all real numbers.
If any real number wants to get from one point to another, it must pass through all integers, fractions and irrational numbers between the two points.
For example, to get from 3 to 4, you have to pass through 3.0001, through 3.1111, through 3.1415926..., through √10, through 3.3333, through... In short, there are all kinds of uncountable infinite numbers.
From this, it is not difficult to find that on this long straight line representing all real numbers, the square (^2) of any point other than the origin (0) will and will only appear at the origin of this straight line (
0), that is, in the category of positive numbers.
For example, the square of the positive number 5 (52) is 25, which is still a positive number and is on the right side of the origin (0).
For example, the square of the negative number -5 (-52) is also 25, is also a positive number, and is also on the right side of the origin (0).
5 and -5, two completely opposite numbers, positive and negative, after undergoing the square multiplication operation process, they got the same number, and it was also a positive number.
Is it amazing?
Of course it's not magical. Positive becomes positive, negative becomes positive, and positive becomes negative. This is a knowledge point taught in the first grade of junior high school.
Then you can imagine, is it possible that there is such a number, whose square (^2) will appear to the left of the origin (0), that is, within the category of negative numbers?
If expressed in another way, it is a negative number, such as -1. Under the premise that there are mathematical rules such as "positive and negative are positive, negative and negative are positive, and positive and negative are negative", can it have a square root, or
How about an even number of square roots?
The answer is: yes.
If this operation is expressed in mathematical language, it is: -1=i2.
To put it simply, i in this equation is the imaginary element.
If a number contains i, then this number is an imaginary number.
But how will the concept of imaginary numbers be reflected in the entire mathematics level, and even in the real world?
The first is the mathematical level.
At this point, it’s time to imagine a second time.
Imagine that in the boundless absolute blank, that long straight line representing all real numbers, the real number axis, is still hanging.
Now, draw a 90° vertical line at the center origin (0) of this infinite and long real number axis.
Let it penetrate the origin and continue to extend (up) along the up and down directions like the real number axis until infinity.
Then this vertical axis perpendicular to the real axis is the imaginary axis.
All numbers that do not exist on the real number axis, such as x in x2 1=0, i in -1=i2, and even square roots of all negative numbers, all exist on this imaginary number axis.
Therefore, this imaginary number axis is the field of imaginary numbers in a broad sense.
In a sense, the real number domain and the imaginary number domain exist in different "phases".
There seems to be no connection between the two, but they seem to complement and 'support' each other.
The plane coordinate system composed of this longitudinal imaginary axis and the transverse real axis, which is infinitely vast in all directions, is the complex plane.
All numbers that exist in this complex plane are complex numbers.
Yes, all positive and negative numbers, all rational and irrational numbers, all integers and fractions, and all real and imaginary numbers are all complex numbers.
Therefore, all realms, domains, objects, and phenomena in the real world that correspond to all complex numbers, the entire positive dimension of reality, the entire negative dimension of nothingness, the entire field of imaginary numbers, and the entire realm of pure emptiness and death are all covered.
in the field of plural numbers.
The complex number field perfectly unifies the two phases of real numbers and imaginary numbers.
As for Mu Cang, who has successfully reached the first level of Aleph, the entire territory he controls is this entire plural domain.
Therefore, Mu Cang, in addition to being an innumerable and infinite being, can also be called... the ruler of the entire plurality of realms.
However, the negative-dimensional abyss corresponding to the negative number system is already emptier than the infinitesimal zero-dimensional point.
The imaginary number system that can multiply two squares with each other and give birth to empty negative numbers will correspond to the field of imaginary numbers in the real world, and to what extent will it be empty?
The answer is... it is much, much, much more void than the so-called ultimate nothingness that all intellectual beings know and imagine.
It can be called absolute nothingness.
But the so-called imaginary number is not imaginary, and everything is unified.
In some respects, the realm of imaginary numbers is not the realm of absolute nothingness.
It contains all the things that have perished, everything that is perishing, and all the creatures and spirits and phenomena in the world of real numbers that have perished, everything that is perishing, and all the creatures and spirits and phenomena that have perished in the world of real numbers. They have appeared in the past, are currently appearing, and will present endless countless infinite species.
The final scene of destruction.
By analogy, it is like the Akasha Catalog, the legendary 'cosmic archive' that contains all the thoughts, words and actions of all intelligent life forms in the past and future at every moment.
The difference is that what is ‘stored’ in the imaginary number field is not the information of all things, but the death of all phenomena in the entire real number field.
So everything in the entire field of real numbers includes a breeze, a bouquet of flowers, a big tree, a mountain, a song, a sword blade, a love, a piece of earth and stone, an ape, a god, a
A black hole, a sea of stars, a universe, a long river of time, an infinite sky... they all already existed in it after death, before death, or even before birth.
At first glance, this seems counterintuitive.
But the weird mechanism in the field of imaginary numbers does not care whether intellectual life can accept it or not.
The world is like this, and the weak can only accept and adapt, but cannot change at all, unless... they are strong enough.
In short, the field of imaginary numbers is the final destination of all entities or non-entities that can be understood and imagined by intellectual life.
As the saying goes, when you are born, you will die, and when you die, you will be born. All things are in one house, and life and death are the same.
Therefore, the field of imaginary numbers can be called the ultimate version of the ‘underworld’.
It's just that in this "underworld", there is no king of hell, no bull-headed horse face, and no ghost soldiers.
And all the "old friends" in Mu Cang's long life, such as Zhang Qiyuan, Kong Bai, Xuanchengzi, Gai Zhoutian, Chu Yingbo, Wu Zhan, Li Yong, Tang Henyu, Monroe Holmes, Mycenae
Er, Xuyuan, Matnu Elis, the Phoenix of Darkness, Yuro, Ogula Fata, Kong Kong'er, King of Gluttony - Xiu, Yuan Zhou Beng, Coo, Wang Chen Jie, Cang Tian Ba
Fist, Zhang Daoxian, Purple Dixon Immortal, Weird Thousand-Eyed Wolf, Supreme Godhead, DC Master Monitor, Lord of Spiritual Consciousness...etc., etc., all exist within the realm of imaginary numbers.
This time, Mu Cang planned to pay them a visit.
Quan should make a final conclusion to the distant journey he is about to embark on.
After it was over, He would never look back and rush towards the endless and distant "poetry and distance" with all his strength.
"What a weird and wonderful world."
Mu Cang slowly walked leisurely with his hands behind his hands in a strange realm that was "extremely vast" without even a trace of space-time structure. He smiled at the corner of his mouth, as if he had seen many interesting things.
In fact, for Mu Cang, the field of imaginary numbers is not as empty as the real number ants imagined, but is much more lively and noisy.
Of course, the so-called 'hustle and bustle' is also defined from Mu Cang's perspective.
He is the highest spiritual being in the entire complex number field. Since he thinks that the imaginary number field is very lively, then it must be very lively here.
But if ordinary real number creatures reach this imaginary number realm, they will find that they are unable to perceive or touch anything at all.
Just because all phenomena in the field of imaginary numbers are incomplete "reality".
All imaginary number phenomena here have two types of structures.
One type is the real part and the other type is the imaginary part.
The imaginary part structure of all imaginary number phenomena cannot have any interaction with each other.
If you want to interact between two imaginary phenomena, you can only rely on the real part structure.
And all these are reflected in the real world. From Mu Cang's perspective, the field of imaginary numbers is "stacked and filled" with endless "dynamic oil paintings".
These 'oil paintings' or pictures are the final scene of the demise of infinite and countless things in the real number field.
Of course, this is also reflected on the mathematical level.
If you want to perform a comparison operation between imaginary numbers and imaginary numbers, you need to use the real part to compare, and nothing can be done with the imaginary part.
Since it can interact, it can be destroyed.
Therefore, if the real structure of an imaginary number event is completely destroyed.
Then, with only the imaginary structure left, it can only helplessly fall into the more abstract realm of pure emptiness and death.
Pure imaginary numbers, as a subset of the overall imaginary numbers, are reflected in the real world - the realm of pure imaginary death, but it is also a "realm of ultimate emptiness" that is even more absolute than the realm of imaginary numbers, which can be called absolute nothingness.
Nothingness exists within it, only the abstract concept of "annihilation" also experiences the "ultimate annihilation" after death.
Apart from that, there is nothing else.
Therefore, after all phenomena with only imaginary structures left fall into this purely abstract realm, they can only and will only become a part of "ultimate destruction", forever integrated into the absolute and endless ultimate destruction.
"A fleeting moment is eternity."
Mu Cang walked to the side of a final scene of destruction, turned around and saw that inside the scene, there were a group of black phoenixes soaring over the long river of time, falling into a hopeless mass extinction.
Yes, they are the Yao Ming Phoenix clan.
What Mu Cang was looking at was one of the Phoenixes in the group who were panicking and trying to escape into the past and future of various timelines.
He suddenly smiled: "I never thought that we would meet here again."
That's right, the giant black phoenix that Mu Cangzhi was looking at was the same one that had shown off its power to him throughout the years.
Mu Cang didn't send the opponent in the picture into pure death, so that would be meaningless.
This black phoenix is already dead, dead is dead, and now it appears in front of Him, it is just the "reappearance of death" of the other party's eternal cycle without beginning or end.
So Mu Cang just thought about it, extracted all "this black phoenix" from all the final scenes of destruction in the entire imaginary number field, and put them into the palm of his hand at will.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! Not only this black phoenix, but also all Mu Cang's 'old friends', such as Yuanzhou Beng, Coo, Cangtian Baquan, etc., also followed.
All of them were extracted by Him from the endless final scene of destruction and put into the palm of his hand.
After that, Mu Cang opened up a space-time world deep in the field of imaginary numbers that has a complex and stable structure but seriously violates the mathematical logic of imaginary numbers, so it should not exist here.
But with Him, all the shouldn’ts become shoulds.
Then, Mu Cang placed all the 'old friends' in this world.
At first glance, they look like motionless dolls of different shapes.
Then, He lightly snapped his fingers:
"Pa~"
After a melodious and crisp sound, all Mu Cang's "old friends" in this time and space world immediately woke up.
"Um?!"
In the vast and unfamiliar world, Xiu, the King of Gluttony, whose body was dark and colorless, and whose eyes were dull and dull, suddenly trembled.
At the same moment, he suddenly escaped from the state of absolute death and suddenly became alive.
Then, Xiu looked around in confusion and found that it was a vast and huge gray arena.
"Uh...I remember..."
He scratched his head with a confused look on his face, "I seem... to be dead, right?"
Xiu's memory still remains at the moment when he was forced by Mu Cang to fall into the singularity of the black hole.
At this moment, a similarly dark and stagnant figure suddenly appeared only a few meters away from him, and also turned to life in the same instant.
"Huh?"
Looking at this tall bloody figure, Xiu asked curiously, "Friend, may I ask who you are..."
While asking, he extended his palm in a friendly manner.
But the tall blood shadow didn't shake hands with Xiu, he just looked at him coldly and said indifferently:
