Review the 8 most important numbers in mathematics

There are infinite numbers and infinite ways to combine and manipulate those numbers. Mathematicians often represent numbers in a straight line. Select a point on this line, this point corresponds to a number. But, almost all of the numbers we use are based on some very important numbers, playing a fundamental role in mathematics. The following are eight essential numbers to perform arithmetic operations.

0

Number 0 represents emptiness. 0 is a basic element in an arithmetic system. We use zeroes in numbers with more than one digit. Number 0 tells us the difference between 2 thousand and 20 thousand dong. The number 0 is called the 'plus element', meaning that if you add a number with 0, you get the result of that number. Example: 3 + 0 = 3.

This property of zero is a central part of arithmetic and algebra. The zero is right in the middle of the arithmetic straight line, with positive numbers and negative numbers on each side, and is the starting point in setting up the number system.

first

If 0 is "plus element", 1 is "kernel element". Take any number and multiply by 1, you have the right result. 5 * 1 equals true 5. Just use 1, we can start to set arithmetic straight lines. Specifically, we can use 1 to get natural numbers: 0, 1, 2, 3, 4, 5, . We can continue adding 1 to create other numbers: 2 is 1 + 1, 3 is 1 + 1 + 1, 4 is 1 + 1 + 1 + 1, . to infinity.

Nearly all of the numbers we use are based on 8 very important numbers.

The natural numbers are the most basic numbers. We use natural numbers to count. We can also perform arithmetic operations with natural numbers: If we add or multiply two random natural numbers together, the result is also a natural number.

In some cases, we also get two natural numbers subtracted from each other, or divided by each other, and the result is a natural number. Example: 10-6 = 4 or 12/4 = 3. Just using numbers 0 and 1 with basic arithmetic operations, we can solve many problems with natural numbers.

-first

It is not always possible to bring two natural numbers except for each other. If there are only counts, we will not be able to express the results of operation 3-8. One great thing about math is that, when encountering such a barrier, we can expand the digital system to eliminate that barrier. To allow such subtraction to occur, we add -1 to the arithmetic straight line.

-1 entails all other negative integers, because multiplying a positive number by -1 produces a "negative version" of that number: -3 is -1 x 3 / By using negative numbers, they We have solved the problem of subtraction. 3- 8 = -5. The combination of positive numbers, 0, and negative numbers we have integers, and we can always subtract two integers from each other and get another integer result. Integers are fixed points on a number line.

Negative numbers are useful in expressing the missing part. If I owe the bank 500 thousand, I can imagine my balance of -500 thousand. We can also use negative numbers with measurements, when values ​​less than 0 can occur, such as temperature. For example, in Sapa, the temperature was down -5 ^o C.

1/10

In terms of arithmetic, integers are not enough. We can add, subtract or multiply two integers and collect integer values, but we cannot get the same result in all cases of dividing two integers for each other. 8/5 is meaningless if we only use integers.

To solve this problem, we use 1/10, or 0.1. For 0,1 and the powers of 0,1 such as 0.01; 0.001; 0.00001; etc. we can show fractions and decimals. 8/5 = 1.6.

Divide any two integers together (except dividing by 0) returns the result as a decimal. If four friends share a cake, each person will get ¼ or 0.25 or 25% of the cake. Decimal numbers help explain the space between two integers in arithmetic straight lines.

In terms of arithmetic, integers are not enough.

√2

The square root of a number is a number that, when squared - when multiplying that number by itself - returns the original number. For example, the square root of 9 is 3, because 3 squares are equal to 3 x 3 = 9. We can find the square root of any positive number, only with some troublesome exceptions.

The square root of 2 is one of those exceptions. This is an irrational number, which means that the decimal part never ends or repeats. The square root of 2 begins with the numbers 1.41421356237 . and the numbers behind do not have any specific rules.

It turns out that the square root of most rational numbers is irrational numbers. Except for a number like 9, called the prime number. Number of bases is very important in algebra, because they are solutions to many problems. For example, the square root of 2 is kicking the sentence for the calculation of X2 = 2.
By combining rational and irrational numbers together, the arithmetic straight line is now complete. The set of irrational and rational numbers is called a real number, and these numbers are used in almost every operation.

Pi (π)

Pi , the circumference of any circle compared to its radius, is probably the most important figure used in geometry. Pi appears in nearly every formula involving circles and spheres, for example, the area of ​​a circle with a diameter of r π x r2.

Π is also used in trigonometry. 2π is the phase of basic trigonometric functions such as sine and cosine. This means that these functions repeat themselves by 2π each. These functions and π play a key role in periodic problems, especially in explaining subjects such as sound waves.

Like the square root of 2, π is irrational, which means that the long decimal part has no rules. The familiar start numbers: 3,14159 . Mathematicians using supercomputers have found 10 billion billions of digits of dù, although for most everyday applications we only Use the first few digits to get accurate results.

Pi, the ratio of any circle's diameter to its radius, is probably the most important figure used in geometry.

Euler constant (e)

The Euler constant , or denoted by e , is the basis of operations with multiple-number functions. Multiplier functions represent expressions that self-duplicate or divide themselves after a certain period of time. If I have 2 rabbits, I will have 4 children after a month, after 2 months, I have 8 children, after 3 months I have 16 children. So, after n months, I will have 2n + 1 rabbit, or 2 self-multiplication with n + 1 time.

e is an irrational number, approximately 2,71828 .; but different from other irrational numbers, the infinite decimal part has no rules. ex is a natural multiplier function, the foundation for any other multiplier function.

The reason ex is particularly troublesome. For those who are familiar with calculus, the derivative of ex is also ex. This means that for any value of x, the exponential increase in the value of ex equals the value of the function itself. With x = 2, ex function increases exponentially by e2. The independent nature of each certain function makes ex very easy to apply in analytic problems.

ex is very useful in multiplier problems. A typical application is to find that the total interest rate is constantly being renewed. For an initial value of P, with an annual interest rate of r, the value of an investment A (t) after t years is calculated by the formula A = Pert .

e ^ x is very useful in multiplier problems.A typical application is to find that the total interest rate is constantly being renewed.

i - √ (-1)

Above mentioned how to be able to extract any positive number, but now try doing it with a negative number. The root of a negative number does not belong to the real number. Multiplying any negative numbers together gives a positive number, so the square of any number will give a positive result, so there is no way to square a real number that can result in a negative number.

But with mathematics, when we meet such a limit, we can extend the coefficient to this type of limit. So, standing in front of the problem that we can't declare base -1, simply suppose if the root of -1 exists. We define i, an "imaginary" unit, as a result of square root -1. And in combination with all these "virtual numbers" , we extend the real number into complex numbers.

Complex numbers have loads of interesting properties and applications. Just as we can represent a real number in a straight line, we can represent complex numbers on a plane, with the horizontal axis representing the real part of that number and the vertical axis representing the "virtual" part, the root of a negative.

Any polynomial equation has at least one result of the complex set. This is extremely important and mathematicians call it a fundamental theorem of algebra . The geometry of the complex number plane has many interesting applications in electrical engineering.