What exactly does meaningful mean when it comes up in mathematics?

What he means is that it is more in line with the doctrine of reality, and it is more connected, life can be better utilized, and some more valid conclusions can be drawn.

The "meaningful" that often appears in mathematics means that the existence of the formula is reasonable, that is, the formula is valid if certain conditions are met, and vice versa.

Mathematically meaningful refers to the conclusion of the axioms of a certain axiom system, or the rules that can be deduced from the axioms of that axiom system. In advanced mathematics 1 0 is infinity, therefore, it makes sense for 0 to be a divisor in higher mathematics. In fact, in higher mathematics, 0 is not allowed as a divisor, and the 0 above is an infinitesimal symbol.

0, it's not zero. To put it simply, both meaningful and non-meaningful can be seen as provisions.

In mathematics, it represents a specific meaning, which is not usually used, but it is generally used in mathematics to find this number.

In mathematics, it represents a new type of operation, which can be addition, subtraction, multiplication, division, multiplication, square, etc. In fact, what mathematics exercises is human thinking, logical thinking, and abstract ability, and the step-by-step development of mathematics is the process of becoming more and more detached from reality from having a practical role.

In ancient China, the nine chapters of arithmetic were all valuable, such as the division of fields, such as the volume of soil used to build the city wall. Therefore, ancient mathematics only stayed at arithmetic, and the calculation system was getting stronger day by day, but the overall progress was not great.

Mathematics is a general means for humans to strictly describe the abstract structure and pattern of things, and can be applied to any problem in the real world, and all mathematical objects are inherently artificially defined. In this sense, mathematics belongs to the formal sciences, not the natural sciences. Different mathematicians and philosophers have a range of opinions on the exact scope and definition of mathematics.

Many mathematical objects such as numbers, functions, geometry, etc., reflect the internal structure of the successive operations or relations in which they are defined. Mathematics is the study of the properties of these structures, for example, number theory is the study of how integers are represented in arithmetic operations.

In addition, it is not uncommon for different structures to have similar properties, which makes it possible to describe their state by further abstraction and then by axioms on a class of structures, and it is necessary to find the structures that satisfy these axioms among all the structures. Thus, we can learn about groups, rings, domains, and other abstract systems.

Taking these studies (through structures defined by algebraic operations) can form the field of abstract algebra. Due to its great versatility, abstract algebra can often be applied to seemingly unrelated problems, such as the ancient problem of ruler diagramming, which is finally solved using Galois theory, which involves domain theory and group theory.

Another example of algebraic theory is linear algebra, which makes a general study of the vector space in which its elements are quantitative and directional. These phenomena show that geometry and algebra, which were previously thought to be unrelated, actually have a strong correlation. Combinatorics is the study of methods for enumerating number objects that satisfy a given structure.

Applied Mathematics and Aesthetics.

Some math is only related to the domain that generated it, and is used to solve more problems in that field. However, mathematics that is generally generated in one field is also very useful in many other fields and can be used as a general mathematical concept. Even the "purest" forms of mathematics usually have practical uses, an extraordinary fact that the 1963 Nobel Laureate in Physics Wigner called "the unimaginable validity of mathematics in the natural sciences".

As with most fields of study, the explosion of scientific knowledge has led to the specialization of mathematics. The main divergence is between pure mathematics and applied mathematics. Within applied mathematics, it is divided into two major fields and has become their own disciplines – statistics and computer science.

Many mathematicians talk about the beauty of mathematics, its inherent beauty and beauty. "Simplicity" and "generalization" are the types of beauty. It also includes ingenious proofs, such as Euclid's proof of the existence of an infinite number of primes; Or numerical methods that speed up calculations, such as fast Fourier transforms.

In his book Confessions of a Mathematician, Goldfi Harold Hardy shows that he believes that aesthetic significance alone is sufficient to justify the study of pure mathematics.

The above content refers to Encyclopedia - Mathematics.

The number of the results of the calculation is meaningless"It refers to the following types of infiltration chains:

1. The "number of scores" does not meet the known conditions;

2. It does not conform to the common sense of life or the common sense of related things;

3. Exceeding the due value range;

"Meaningless" in the calculation process refers to ":

1. The denominator of the fraction is zero;

2. The number of open and even power is negative;

3. Logarithmic function.

The true number of 0;

4. Power exponent.

power 0 in 0;

Except for these cases, the rest generally makes sense.

But the definition of this distinction is also very complicated, classified as junior high school mathematics or high school mathematics or college mathematics, the meaninglessness of mathematics at different stages is different, for example, when the discriminant formula of a quadratic equation is less than zero, it is meaningful after learning complex numbers, and the denominator is zero after learning linear equations.

After that, it makes sense.

Introduction: When students are generally solving math problems, they will find that the math problems are generally required to be meaningful, what does this meaningful mean? Let's find out.

<> for many students, it is particularly troublesome when solving some practical problems or big problems in mathematics, because there will be many conditions for him, and there will often be three words meaningful, in fact, he wants to make this problem or this formula have a certain degree of rationality, so that this problem is meaningful, so we must meet the conditions to be met in order for this problem to be valid, otherwise it will not be valid. Let's take an example today, that is, the numerator and the denominator, we must know that the denominator cannot be 0, so it is a non-0 natural number, how to make this formula meaningful at this time? This is the condition that it needs to meet, and when I meet these conditions, this set of problems can be solved, so a lot of meaningful means that certain conditions need to be met before we can solve this problem.

So when you do the problem, you must meet the requirements of the formula, at this time some mathematical formulas can help students solve the answer, when you find that you do not meet the requirements of the formula, in many cases the formula is unsolvable, so even if you write a paper, its possible results are still not known, so we must carefully and carefully put forward its rationality when doing the problem, so we must meet its conditions, so that there can be a solution. Because you will know that there are generally many formulas in math problems, and the range of formulas may be very wide, so literally we understand the meaning is to make the equation true, but when doing math problems, we know that many problems can not be virtual, it is closely related to our reality, at this time we must know how to meet some conditions in reality, so anything can not be 0, when it is 0 we solve the answer may be unsolvable.

The meaning is what kind of feeling is expressed in this question, what kind of meaning is expressed, and what kind of result can be obtained in this question, which is the meaning of meaning.

Specifically, within a certain range of functions, there must be corresponding values.

The meaning of math functions in this problem, math problems are very interesting, and people who are good at math generally have good brains.

Summary. Dear,"!Represents a factorial symbol that usually follows a natural number.

Such as 3!＝3×2×1,5!＝5×4×3×2×1．0!

In mathematics, the value is specified as 1, i.e. 0!1 We call a function of the form y a x (where x is an independent variable, a is a constant, and a 0, a≠1) a logarithmic function such as y 2 x and y = ,..., etc. Hope it can help you.

What does it mean in mathematics?

Dear,"!Represents a factorial symbol that usually follows a natural number. Such as 3!

3×2×1,5!＝5×4×3×2×1．0!In mathematics, the value is specified as 1, i.e. 0!

1 We call a function of the form y a x (where x is an independent variable, a is a constant, and a 0, a≠1) a logarithmic function such as y 2 x and y = ,..., etc. Hope it can help you.

Dear,"!In mathematics it is denoted a double factorial product. Double factorial is a mathematical concept that uses n!!

Denote. The double factorial of a positive integer represents the product of all positive integers that do not exceed this positive integer and have the same parity as it. The double factorial of the first 6 positive integers is:

3，4!!=8，5!!=15 and 6!!

48。Such as 12!!=12×10×8×6×4×211!!

There are many kinds of animals living on the earth, but human beings are the most special, because we have our own culture, emotions, etc., in order to build a huge human empire, in daily life, education is essential, it is precisely because of the spread of culture that the world is changing with each passing day, changing all the time, many people hate mathematics in the reading stage, and even never get a high score, because it is too difficult for them, especially there are many definitions in mathematics, such as math problems" What does it mean to be meaningful? He has a literal meaning and a question cover, such as the original literal meaning of something we want to do something meaningful, and the math problem is to prove whether a certain method or thing is feasible, and if you can get a satisfactory result, then the grinding opens up another space.

With the development of education, people's cultural level is getting higher and higher, and they are engaged in high-level work in various industries, and mathematics has been changing our lives since its birth thousands of years ago, such as the algorithms we usually use to buy things, various computer programs, and even every item we use around them. Usually we think that it is to see whether a certain method or conclusion is correct, such as where a certain point passes, and proves that it is meaningful, then it means that the point does pass through this place, and then it is a judgment that is meaningful, and it is a judgment that is right or wrong in the current era, such as Newton's law of universal gravitation, which has not been denied for hundreds of years, but whether it will not exist in a different space requires another judgment. Therefore, we can unanimously understand that meaning in mathematics is a judgment of what is feasible or not.

From ancient times to the present, many mathematicians have emerged all over the world, they have helped the development of the whole era, and they are also the pioneers of mankind, and we need to continue to study and explore in order to make human beings develop better, so the meaningful exploration of mathematics is the exploration of the future of mankind. <>

What does "meaningful" mean in mathematics?In fact, in mathematics, "meaningful" means that within the limits of definition, it meets the regulations, requirements or restrictions, and vice versa.

1.The denominator of a fraction or fraction cannot be zero, and the divisor of a fraction or fraction cannot be zero, because zero is infinitesimally small, and if a constant is divided by an infinitesimal quantity, then it is meaningless, and zero cannot be the denominator, and if zero is the dividend, zero divided by zero equals zero, and any multiple of zero is equal to zero, then this is meaningless, and therefore zero cannot be used as a divisor, so mathematically it is stipulated that the denominator and divisor of fractions cannot be zero.

2. In the range of real numbers, the value of the quadratic root formula cannot be negative, the quadratic root is non-negative, the square root of the arithmetic is non-negative, the square root of a positive number has two zeros The square root is zero, and the square root of the arithmetic is non-negative, which is the double non-negativity of the quadratic root, if the square root of a negative number is still a negative number, the square of the negative number cannot be a negative number, otherwise it will be meaningless, so it is stipulated that within the range of real numbers, the quadratic root requires that the square number cannot be a negative number, but can only be a non-negative number, a positive number and a zero.

3. Mathematically meaningful is actually the existence of a formula, and it must have its rationality, that is, the letters that satisfy the validity of this formula are all satisfied and established.

In fact, it is not only "meaningful" in mathematics, but also "meaningful" in reality, for example, we eat, the meaning of eating is to fill the stomach, if we are full, we should eat, and it is meaningless to eat, for example, someone needs your help, you did not help her at that time, after a long time, other people's problems have been solved, and it is meaningless for you to help her, if it does not conform to the common sense of life, nor does it conform to the common sense of related things in life, everything you do is meaningless, only to meet the conditions at that time, Things will "make sense".