If the math and logic are good, come in, and don t make a fool of the rest

Still consider the function f: mathbf longrightarrow mathbf assumes c is f

defines the elements in the domain. Function f

It is said to be in C

The point is continuous if and only if the following conditions are true:

As long as x satisfies c- delta, there is.

f(c)- Valebsilon was established.

Is that the definition?

You can make the inequality in the problem y=c

Artificially take a delta to satisfy the delta

Just point out that delta exists, and there is no need to find delta

This function satisfies the Lipositian condition, so it is continuous.

f can take |x|So|f(x)-f(y)|=||x|-|y||<=|x-y|(This uses the absolute inequality |.) |a|-|b| |a土b|≤|a|+|b|)

From the point of view of the graph, continuity means that the function has no discontinuity, and at a certain point it is derivable, that is, it is smooth at this point, not a sharp point, f(x)=|x|At x=0 is a sharp point, so it is not derivable.

The existence of a certain point limit has nothing to do with the function value of that point, and continuity is related to the function value, but it is a stronger condition.

I think math and logic are good, but English is too scumbag.

No problem, that's the second answer.

In 1, 4 is a multiple of 2. The same goes for expansion.

Of the 3, 10 is a multiple of 5. The same goes for expansion.

2, inversely: if n is a multiple of 5, that is, n=5*x, then the left and right sides are multiplied by n at the same time, and the square of n = 5*x*n, and the right x*n must be an integer. So it's all correct.

One and three are correct. Second, the method of counter-evidence can be used. Hypothesis. The square of n is five, then n is the root number five, not a multiple of five.

Through observation, it was found that there was no repetition.

So 2*2*2*5*3-1=120-1=119 kinds.

The fourth is correct, which can be found by enumeration.

Summary: A deep understanding of the application of mathematics in life. At the same time, using the knowledge I learned, I solved a lot of problems in real life.

This semester's mathematics study not only increased my knowledge, but also stimulated my interest in learning mathematics, and I will work harder to study mathematics and apply mathematics in the future!

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.

Mathematical Logic:Mathematical logic focuses on placing the number guessing back school on a solid axiomatic framework and studying the results of this framework. For its part, it is the source of Gödel's second incompleteness theorem, which is perhaps the most widely circulated achievement of logic Modern logic is divided into recursive theory, model theory, and proof theory, and is closely related to theoretical computer science.

Encyclopedia Mathematics.

The past year has been full of ups and downs, joys and sorrows. In what used to be a classroom, all the emotions fluttered and danced, filling the whole semester. Now that's just the past, or worse, because we can't go back.

During this semester, I will do my best to study to achieve my future goals and ideals. I look forward to the future, embrace the future, and look forward to the future. "There is a diligent path in the book mountain, and the bitter sea is endless.

You can. Goal, sprint 630! In the face of goals, first of all, face learning with a good attitude.

Challenge yourself and believe in yourself. Secondly, one point that cannot be ignored in learning is to learn to analyze one's own learning characteristics, and one point that cannot be ignored is to learn to analyze one's own learning characteristics.

My reasoning skills are okay, but I always feel too difficult and boring for some things that can only be learned by rote, which is my shortcoming, and I will overcome it in the first semester of junior high school. Finally, and most importantly, it is necessary to arrange time scientifically, without reasonable arrangement, no matter how good the plan is, it will be in vain. Efficiency is always important in my planning.

First, it is necessary to make reasonable arrangements for study, recreation, and rest time, and to grasp every bit of precious time. Second, set aside a part of your time to exercise, for yourself and for better study.

Logic

Main article: Mathematical logic.

Mathematical logic focuses on placing mathematics on a solid axiomatic framework and studying the results of this framework. For its part, it is the source of Gödel's second incompleteness theorem, which is perhaps the most widely circulated result of logic Modern logic is divided into recursive theory, model theory, and proof theory, and is closely related to theoretical computer science.

The above content reference: Encyclopedia - Mathematics.

Mathematical logic is similar to mathematical logic, also known as symbolic logic and theoretical logic. It is both a branch of mathematics and a branch of logic. It is a discipline that studies logic or formal logic with mathematical methods.

The object of study is the formal system after the symbolization of the two intuitive concepts of proof and computation. Mathematical logic is an indispensable part of basic mathematics. Although the word logic is included in the name, it does not belong to the category of pure logic.

I think mathematical logical thinking definitely refers to reasoning ability. , that is, what conditions are known, and then a certain result can be deduced, this is the ability of logical reasoning.

My classmates are all studying in Japan from graduate school to doctoral degree, and I especially like mathematics, and when I talked about children's education recently, I suggested that I study logic now.

It is a typical phenomenon: logic is not offered to science and engineering students in China, which leads to the omission of some key steps in the thinking process, and only the result is seen in the learning process, regardless of the process. So a lot of people do math by brushing up on questions.

UNESCO has defined seven basic disciplines: logic, mathematics, astronomy, chemistry, life sciences, astronomy, and geography.

In Europe, the United States, and Japan, the first subject to be taught before learning mathematics is logic. The students said that they felt that they had encountered a ceiling in academic research recently, and the main reason was that they did not learn the basic discipline of logic well, so when they learned mathematics, they couldn't make a mess of the stool and take out reasoning.

Many concepts are limited to prescripts, for example, when learning sets, we all know that empty sets belong to any set, and the teacher did not give an inference at the beginning, only said that it was prescribed, and in fact this conclusion is deduced through logic.

What aspects of mathematics does logic influence?

Mathematics is a science with a high degree of abstraction and rigor, and the correctness of its formulas, theorems, laws, principles, etc., cannot be proved by concrete experiments and empirical practice, but can only be confirmed by strict deductive argument logically.

Without logic, the edifice of mathematics cannot be built, or at least the axiomatic deductive mathematics of the system cannot be constructed. That is, mathematics in the modern sense is impossible to exist.

From the perspective of the emergence and development of mathematics or one of its branches, the development of mathematics has its own laws, but its development stage is also accompanied by the development of logic. It embodies the results of human thinking and ingenuity.

The formation of mathematical theories requires a process of accumulation of relevant empirical materials, then enters the stage of refining and sorting, and then goes through organization and selection of rough fingers, and finally forms a set of systems. There is no doubt that logic needs to be applied throughout the process (inductive logic in the initial stage, and evolutionary logic in the collation stage).

Looking at Douyin, I found that there are really a lot of courses on logical thinking, and I am glad that some people have realized the importance of logic.

But I do know very little about logic, and I plan to seriously study the basics of logic for children aged 3-6.

Let's talk casually: 1) If a+b=a+c is known, then b=c, is it correct and why? If a is 0, then b is not necessarily equal to c.

2) If ab=bc is known, then b=c, is it correct and why? In the same way, if a is 1, then b is not necessarily equal to c.

3) If a+b=a+c, and ab=ac, then b=c, is it correct and why? Regardless of whether a is 1 or 0, b must be equal to c

1) Correct, according to the mathematical formula there is such a theorem.

2) Incorrect If a is 0, b=c does not wait for 0, it will not be correct.

3) Correct mathematical theorem.