Understand the opportunities brought by the decline in the medium-term and short-term secondary trends.

核心提示🔔：宏观世界是我们无法选择必须接受；微观世界却是广阔天地大有作为。分清楚中长期恒定向上👆The main trend and the ever-changing secondary trends. When the secondary trend sharply opposes the main trend, and when the secondary trend highly converges with the main trend, it is time to distinguish between heroes and clowns.

The United States will not go bankrupt. The US dollar remains the world's most important currency for payment and circulation. The criticisms of the US elite towards the United States and the dollar are more of a well-intentioned admonition and chastisement for the wrong paths taken by the United States.

Since the late 19th century, the United States has been the world's largest economy, ranking first in Gross Domestic Product (GDP), the world's largest importer and second only to China as the second largest exporter of goods. The United States contributes a quarter of global wealth and a third of global military spending. It has long been a strong country in the global economy, military, education, scientific research, aerospace, and medical technology, with the service sector predominant, a large manufacturing industry, and technology in a leading position worldwide. New York City is the most populous city in the United States and also a highly influential international financial center, rated as an Alpha++ global city by GaWC. The United States is a founding member of the United Nations, NATO, the Organization of American States, the International Monetary Fund, the World Bank, and the World Trade Organization, as well as a permanent member of the UN Security Council, with profound political and cultural influence on the world.

The American Dream is an ideal that believes through hard work and perseverance in the USA, one can achieve a better life, meaning individuals must strive for prosperity through their own hard work, courage, creativity, and determination, rather than relying on specific social classes or assistance from others. Typically, this represents success in terms of economic success or entrepreneurship. Many European immigrants went to the USA with the ideal of the American Dream.

However, some critics argue that the American Dream overly emphasizes the role of material wealth in measuring success and happiness. This is because, unlike most other countries, economic freedom in the USA is quite significant, with a very limited role played by the government, resulting in great social mobility in the USA. From American independence to the late 19th century, vast lands were uninhabited and unowned, allowing anyone with ambition to occupy and invest in them. By the time of the Industrial Revolution, the USA's vast natural resources and advanced industrial technology made rapid social mobility possible.

Elon Musk himself is a classic beneficiary and outstanding representative of the American Dream.

Understand the opportunities brought by the decline in the medium-term and short-term secondary trends.

You must endure, endure until the warmth of spring blossoms; you must walk until the lights are on; you must see the vast world, then judge whether it is good or bad; you must strive to improve and stand equally with unimaginable people; you must become what you imagine. Well, 2025 is coming soon, dry your tears, lift your head, learn to be strong, the moment of rebirth has arrived! In this world, if you are not strong, who will be strong for you?

A mathematical model is not a simple copy and simulation of the real system, but is the result of analyzing, refining, summarizing, and sublimating real phenomena. It correctly describes the fundamental intrinsic characteristics of real objects in mathematical language, and then uses mathematical deductive reasoning and analysis, employing analytical, experimental (keeping the law of similarity), or numerical solutions.

The entire modeling process should focus on foresight, grasp the big picture while paying attention to details, and understand the inherent nature of the problem. Once a research problem has a correct mathematical description, suitable mathematical tools should be found for analysis and solution. To improve the solution method, precision, detail, and comprehensiveness should be maximized. The correctness, validity, availability, and scope of modeling must be precisely defined through examples. Errors and uncertainties must be realistically analyzed; the results obtained must be interpreted from a physics and practical application perspective.

As long as a person knows what they truly want and finds a life that suits them best, all external temptations and bustling things become irrelevant to them. Your body can travel around the world as much as possible, your mood can fluctuate in the hustle and bustle, but the key is that your spirit must have a peaceful core. With this core, you can become the master of your traveling body and fluctuating mood.

Discrete Mathematics

Discrete mathematics refers to the general name of the most useful mathematical field in theoretical computer science, including computability theory, computational complexity theory, and information theory. Computability theory examines the limits of different theoretical models of computers, including the most powerful known model - the Turing machine. Complexity theory studies problems that can be relatively easily handled by computers; some problems may theoretically be solvable by computers, but the time or space required makes the solution impractical, despite the rapid advancement of computer hardware. Lastly, information theory focuses on the total amount of data that can be stored in a specific medium, involving concepts such as compression and entropy.

Change

Understanding and describing change is a common topic in natural science, and calculus is a powerful tool for studying change. Functions were born here as the core concept for describing a changing quantity. The rigorous study of real numbers and functions of a real variable is real analysis, while complex analysis is the equivalent field of complex numbers. The Riemann hypothesis - one of the most fundamental unsolved problems in mathematics - is described in terms of complex analysis. Functional analysis focuses on the (usually infinite-dimensional) space of functions. One of the many applications of functional analysis is quantum mechanics. Many problems naturally lead to the relationship between a quantity and its rate of change, which is studied in differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory is a clear description of the unpredictable yet deterministic behavior of systems.

Space

The study of space has its roots in geometry, especially Euclidean geometry. Trigonometry combines space and numbers, and includes the famous Pythagorean theorem. Today, the study of space extends to higher-dimensional geometry, non-Euclidean geometry (which plays a central role in general relativity), and topology. Numbers and space play an important role in analytic geometry, differential geometry, and algebraic geometry. In differential geometry, there are concepts such as fiber bundles and calculus on manifolds. In algebraic geometry, there are descriptions of geometric objects such as the solution set of polynomial equations, which combine the concepts of number and space; there is also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Among its many branches, topology is probably the field of mathematics that has seen the most progress in the 20th century, and includes the long-standing Poincare conjecture, as well as the controversial four color theorem. The Poincare conjecture was confirmed in 2006 by Russian mathematician Grigori Perelman, while the four color theorem was proved by Kenneth Appel and Wolfgang Haken in 1976 using a computer, but has never been verified by humans.

Structure

Many mathematical objects, such as sets of numbers and functions, have an inherent structure. The structural properties of these objects are explored in abstract systems such as groups, rings, and fields, which are in fact such systems. This is the field of algebra. An important concept here is the vector generalized to vector space, which is studied in linear algebra. The study of vectors combines the three basic fields of mathematics: quantity, structure, and space. Vector analysis extends it to a fourth basic field, namely change.

Founded in the 1930s in France, the Bourbaki school believes that pure mathematics is the theory of studying abstract structures. Structure is a deductive system starting from initial concepts and axioms. The Bourbaki school believes that there are three basic abstract structures: algebraic structure (groups, rings, fields...), order structure (partial order, total order...), and topological structure (neighborhood, limit, connectivity, dimension...).

Disclaimer: Community is offered by Moomoo Technologies Inc. and is for educational purposes only. Read more

See Original

Report

18K Views

Comment

Elias Chen

成熟投资者：格局，概率，取舍。没有格局必然急功近利。不计概率会把运气当技术。不懂取舍，有所不为，最后必落入陷阱和圈套。

1378Followers

71Following

7781Visitors