Such as the title Infinite symbolic representation, English pronunciation

I don't know if you can go to Wikipedia. The following article is from there, but some symbols and mathematical equations can't be pasted because they are pictures. You'd better go to this website by yourself
Infinity, or infinity, comes from the Latin infinitas, which means "without boundary". It has different concepts in theology, philosophy, mathematics and daily life. The term is usually used without referring to its more technical definition
In theology, for example, in the works of the theologian Duns Scotus, the infinite energy of God is used in unconstrained, not infinite quantity. In philosophy, infinity can be attributed to space and time. In theology and philosophy, infinity is discussed in many articles as the paradox of infinity, absoluteness, God and Zeno
In mathematics, infinity is related to the following topics or concepts: limit of mathematics, Aleph number, group in set theory, Dedekind infinite group, Russell paradox, hyperreal number, forward-looking geometry, extension of real number, and absolute infinity. In some topics or concepts, infinity is considered as a concept that increases beyond the boundary, rather than a number
In terms of popular culture, we have bass Lightyear's cry: "go to infinity and surpass!" which can also be seen as the cry of set theorists who study large cardinal
[editor] history
[editor's] early views on infinity
The earliest record of infinity appeared in Yajur Veda (1200-900 BC) of India. The book says, "if you remove or add a part of infinity, the rest is infinity."
Surya prajnapti (C. 400 BC) divides numbers into three categories: countable, uncountable and infinite
*Countable: small, medium and large
*Incalculable: close to incalculable, truly incalculable and incalculable
*Infinity: approaching infinity, real infinity and infinity
This is the first time that the idea that infinity can be classified appeared in human records
From Renaissance to modern times
Galileo was the first to find that a set can have the same size as its proper subset. He used the concept of one-to-one correspondence to show that the set of natural numbers {1,2,3,4...} is as much as the set of square numbers of subsets {1,4,9,16,...}, that is, 1 → 1,2 → 4,3 → 9,4 → 16
One to one correspondence is a necessary technique for studying infinity
Infinity in religion
Buddhism: limitless longevity, limitless light, limitless a Seng, limitless hundred million robbers, four limitless hearts - kindness, compassion, joy, sacrifice, limitless beings, law, limitless vows, boundless suffering. Taoism: limitless heaven, limitless man, limitless merit
Infinity in Philosophy
Infinity in Mathematics
Infinity in real analysis
In real analysis, the sign, called "infinity", stands for unbounded limit. It means that x exceeds any given value, and X is ultimately less than any given value. When the points marked as sum are added to the topological space composed of real numbers, two-point compactness of real number set will be produced. By adding algebraic properties, we get super real number. We can also take sum as a point and get one point compactness of real number, In projective geometry, infinite line is introduced in plane geometry, and similar concepts are also introduced in higher dimensions
Infinity is not only used to define limit, but also can be used as a value of extended real number set in real number analysis
It means that the value range of T in the image of F (T) function is more than limited, and t is equal to 0 to 1
It means that the area of F (T) function image in the range of specified value increases with the infinite increase of its upper limit
It means that although the upper limit of F (T) function is infinitely increased, its image area is still equal to 1
Infinity and infinitesimal
Generally speaking, infinity refers to infinity, but infinitesimal is also a kind of infinity. Through the mapping of y = 1 / x, infinity can be mapped to infinitesimal. In calculus, the concept of higher-order infinitesimal is commonly used
Infinity in set theory
There are different definitions of infinity in set theory. German mathematician Cantor proposed that the number of elements (cardinal number) corresponding to different infinite sets have different "infinity"
The only way to compare different infinite "sizes" here is to judge by whether one-to-one correspondence can be established, instead of Euclidean view that "the whole is greater than the part". For example, because integer sets and natural number sets can establish one-to-one correspondence, they have the same infinite cardinality
For example,
The cardinality of countable set, such as natural number set, integer set and even rational number set, is defined as alef0()
Those larger than a countable set are called uncountable sets. For example, the cardinality of a real number set is the same as that of a power set of natural numbers
Since the power set of an infinite set always has a higher cardinality than itself, it can be proved that the number of infinite cardinalities is infinite by constructing a series of power sets. However, it is interesting that the number of infinite cardinalities is more than any cardinality, so it is an "infinity" larger than any infinity, and it cannot correspond to a cardinality, Otherwise, there will be a form of Cantor paradox

Music and my life
chinese

A writer once said: "if you want to thank someone, and only once, then I want to dedicate this time to those who create wonderful music for human beings. If there is no music, our life will become so boring and terrible." I grew up in my mother's hypnotic music. When I grew up, I became inseparable with music
In my mother's eyes, I am a musical genius. I remember when I was in kindergarten, my teacher once taught us to sing a children's Song - "Twinkle, twinkle, Jingjing". During the play, I played out the melody of this song with a toy harp. The whole family was very surprised. From then on, they took me into the palace of music and let me enjoy the charm of music, Since then, I have become addicted to playing piano. Through the cultivation of teachers and parents, I have reached piano grade 8
Beautiful music, like rain, moistens my heart. It's not language, but language
Whenever I play "memories of childhood", the melody is sometimes slow, just like the gurgling stream; sometimes cheerful and lively, as if to bring me to the childhood full of dreams, we are playing along the colorful river. Whenever I play "wedding in a dream", the fresh chord, like the melody of song, bursts out from my fingertips, like a crystal spring, Silently washing the dirt of my heart. Unconsciously, I can't help but indulge in the wonderful music. When Strauss's "Blue Danube" floats by my ears, I can't help but let my fingertips dance on the keys with the melody
Whenever I play the band eight grade examination repertoire "embroidered gold plaque", the hard-working, simple and kind peasant women are all displayed in front of me one by one
Whenever I play Beethoven's symphony of fate, the tragic melody and the spirit of challenging doom shock me, and the knock of fate reverberates around me
Music, your charm is so amazing! I love music, and my dream of pursuing music will never stop

How to change kilowatt hour into kilowatt hour

Kilowatt and kilowatt hour are two different dimensions; kilowatt is the unit of power (representing how much energy J / S is consumed per hour, minute, or second); 1W = 1 joule / S; 1000W = 1000 Joule / S; kwh is the unit of electric energy, which can be converted into international unit Joule J

It is known that the area of a rectangle is 3a2-3b2. If the length of one side is a + B, then its perimeter is a______ ．

(3a2-3b2) / (a + b) = 3 (a + b) (a-b) / (a + b) = 3a-3b. The perimeter can be obtained as: 2 [(a + b) + (3a-3b)] = (8a-4b). Therefore, (8a-4b) should be filled in

The energy meter of Xiaoming household appliance is marked with "1200R / kW · H". When the electric furnace is only allowed to work alone, the electric power of the electric furnace will be zero if the aluminum plate rotates 30 revolutions in 2min______ W．

Electric energy consumed by electric furnace: w = 301200kw · H = 140kW · h, at this time, electric power of electric furnace: PST = 140kW · h260h = 0.75KW = 750W

The shadow length of a person is 0.8 meters, the height is 1.2 meters, the shadow length of the street lamp is 6 meters, and the height of the street lamp is how many meters?

The height of street lamp is x meters
1.2∶0.8=x∶6
0.8x=1.2×6
x=7.2/0.8
x=9
The height of the street lamp is 9 meters

The heat is the heat__ Its symbol is_ The unit is____ .
The amount of heat absorbed or released by an object is related to [], [], and []
The specific heat of a substance is related to the mass, the temperature of the object

Heat refers to the amount of heat absorbed or released by an object. Its symbol is (q) and its unit is (J)
The amount of heat absorbed or released by an object is related to the specific heat, mass and the increase or decrease of temperature
The specific heat of a substance has nothing to do with its mass, has nothing to do with the increase or decrease of its temperature, and is only related to the substance itself

The mass of the spring vibrator is m, and the spring stiffness coefficient is K. a wooden block with mass m is placed on the vibrator to make the vibrator and the wooden block vibrate harmoniously on a smooth horizontal plane. As shown in the figure, the restoring force F of the wooden block is provided by the static friction force of the vibrator on the wooden block. If f = - K ` x, X is the elongation (or compression) of the spring, Then K '/ K should be: A, M / M B, M / (m) C, (m m m) / M D, M / m

To move on a smooth plane is to ignore friction
The force analysis of wood block is only affected by gravity and static friction. The static friction provides acceleration, K ` x = ma
The force analysis of wood block and spring vibrator is only affected by spring tension and gravity, KX = (M + m) a,
In conclusion, K '/ k = m / (M + m)

When a capacitor and a resistor are connected in parallel in the circuit, how do the current and voltage of the capacitor and the resistor change?

The voltage of the resistor changes directly to IR
Although resistance and capacitance are connected in parallel, the voltage of them is equal, but the voltage of capacitance cannot be transiently changed. Therefore, the voltage of capacitance gradually increases and finally becomes IR, which is equal to the voltage of resistance

If the mass of the car is m, the horizontal curve is a circular arc with a radius of 50m, and the maximum static friction between the car and the ground is 0.2 of the weight of the car. What is the maximum speed of the car when driving in the curve to make the car not skid when turning? (take g =)

The car is in circular motion. The research object of this topic is the car in circular motion. The circular track of the car in circular motion is on the horizontal road, and the center of the circle is the center of the arc, with a radius of 50m. The stress analysis shows that the car is subject to the vertical downward gravity and the vertical road upward elastic force, pointing to the axis of rotation

Such as the title Infinite symbolic representation, English pronunciation