In some special cases, if it is greater than or equal to 1, only one number can be restricted, such as 5, then 5 must be greater than or equal to 1, and all conditions are met. Therefore, it seems that the previous existence is redundant. However, after you go to college to study more complicated mathematics, it is difficult to prove that more and more problems directly equal this relationship. In other words, it's just hard to prove. Generally speaking, we prove that one is greater than or equal to, and then the other is less than or equal to. When the range of the two is infinite, a value can be obtained. For example, I have to eat more than three bowls of rice to be full. There are more than three bowls of rice, but there are only three bowls of rice left at home, so I eat three bowls at most, that is, less than or equal to three bowls. Therefore, when I am full at home and satisfy 3 and 3 at the same time, I can conclude that I just ate 3 bowls of rice.
This expression is common in solid geometry. If there is a point outside the plane and only one plane is parallel to this plane. It first emphasizes that there is a plane passing through this point, but there are infinitely many such planes. If you want to be parallel to a known plane, there is only one plane. If not limited, it can be considered that there are at least two such planes parallel to the known plane. On the other hand, without this, the context will not be fluent and its logical rigor will be greatly reduced.
Do you have a girlfriend?
I have one, and only one.
"You" means that a girlfriend "exists" and is an affirmation of having a girlfriend; "Only" means he is single-minded, he has no feet!
This is where mathematics needs to be more precise.
Yes, that means it must exist.
Only, which means only exists.
It means, here, it means gradual emphasis. When necessary, the above two conditions are met simultaneously.
Literally, just. There are two meanings, yes, only one. From the Chinese point of view, no problem.
However, mathematics has its own unique expression, or terminology, which is fixed like mathematical symbols.
So, I advise you to respect him.
Conclusion: It cannot be changed. Because it is an idiom, it embodies seriousness and professionalism.
What can be described by symbols should not be described by language!
Being is being.
What is the symbolic representation of existence?
What is the only symbolic representation? !
You can give many corresponding descriptions of "only" and "only" in the vast China writing culture, which are all right, but only symbols are unique, universal and unambiguous.
Mathematical language is rigorous, which is different from the language in life.
Life is only "unique" and the meaning of "existence" can be truly deduced. "Do you have a house? Only one set. " Anyone can judge this fact.
In mathematics, "you" is a layer of meaning, called existence; "Unique" is a higher meaning, meaning "unique". Sometimes it is only necessary to investigate the existence, and sometimes it is necessary to further investigate whether it is unique.
Contemporary mathematics works are all translated from foreign languages. For the sake of strict equivalence, the first translator translated like this. It has been established for many years and cannot be changed. Not only do these make you feel uncomfortable, but there are many other inverted sentences in advanced mathematics that do not conform to the language norms of our country, such as "We say so-and-so is ... if the conditions are met ..." Mathematicians do not understand Chinese. In fact, many mathematicians are very accomplished in Chinese.
To learn mathematics, just follow the laws of mathematics.
This is the relationship between necessary conditions, sufficient conditions and necessary and sufficient conditions. There is a necessary condition and only one sufficient condition, which constitutes a sufficient and necessary condition. Its existence and the result of expression are mutual. If useful is removed, it can only show that most results can be reciprocal, but they cannot be reciprocal under certain conditions. In mathematical terms: yes and only = yes. Yes and only refers to certainty, no doubt and no ambiguity. Having or having only a single expression is mathematically inaccurate and imprecise. For example, there is only one straight line between two points, and a straight line is determined between two points. These two sentences have exactly the same meaning and can be replaced with each other without ambiguity. It means that there must be a straight line between two points, and there must be only one, not two or more. Look again, there is a straight line between the two points. This sentence alone is not wrong, but it is not the only one. Continue: There is only one straight line between two points, which is not wrong and also indicates uniqueness. But from the point of view of mathematical logic, it is not rigorous, because it is not based on the foundation, not progressive, that is, it is not based on this necessary condition. So this sentence cannot be used as an axiom. Mathematics is the most logical subject, and there can be no ambiguity at all. An irresponsible person feels a little casual, and some just feel like the backbone, which is very certain. So one can't be an axiom and the other can be an axiom.
I saw a group of people pretending.
Lu Xun wrote two famous jujube trees, and a group of people said that he wrote sick sentences.
Mathematicians say "sick sentences" in unison, and a group of people come to sophistry and tell those fabricated fallacies. Even the "necessary and sufficient conditions" of mathematics are made up by him.
Yes and only semantically, like two jujube trees, it is a sick sentence. But in terms of logical order (progressive relationship), it is a progressive relationship, just like two jujube trees (the spatial transformation relationship of observing trees on the spot). There is not only whether there is, but also the semantic relationship of "what is there and how much is there". Look at the three phrases "You, You, How Much" respectively. Do you find any logical connection and significance between them? Yes, it is a logical progressive relationship.
Really? Yes
What's there? There is a solution. Is there a tree or a jujube tree? )
How many? There is one and only one. (There is one, there is another)
It can't be changed from the point of view of mathematical proof! "You and uniqueness", or "You and uniqueness", has two meanings, indicating existence and uniqueness. When you prove it, you should prove two meanings, sufficiency and necessity! Only China people's habits can express two kinds of meanings, but logically it is only a layer of meaning, indicating uniqueness, not existence. In addition, when expressing uniqueness, only feeling is stronger than only emotion, so it is often used in literature. In natural logic, only "only" and "only" must be added before it. This may be a translation of concepts that existed in western logic from the beginning. Of course, if logic originated in China, then we can use "only" or "only". Who let us be followers? This is purely a personal opinion, or speculation! I haven't read western English classics! I just hope we can create a creative classic!
I asked you where you came from, and you said you were from Ersha Village, but you didn't say which country, province, city, county or township. Let you talk, but you just don't. The reason is that I said village. Doesn't this information include provinces, cities, counties and townships? Well, your logic is very strict, but I always think you are an idiot. Why?