Mathematical concepts are abstract, but important core concepts are not deliberately created by mathematicians, otherwise mathematics does not belong to natural science.
"Set" and "number" are very similar and belong to the fact that human beings have to admit. Like the four operations and calculus, this is not an invention but a discovery.
Aliens can live without humans, but they can't live without mathematics. Their language, appearance and lifestyle may be beyond our imagination, but they will certainly count.
In the middle of last century, the United States launched the Earth Messenger-Voyager spacecraft and went into the vast space to find aliens. The name card of the earth is the language of mathematics, because only mathematics is the universal natural language of biology.
In order to distribute and manage prey, ancient humans had to make statistics and evolve into natural numbers. After agriculture came into being, they measured the land and gave birth to geometry.
Later, the more and more complex things people pay attention to, the more they should consider the whole and the parts separately. This is the thinking of analysis and induction, thus forming a collective feeling.
Numbers have four operations, and sets also have four operations (union, difference, intersection and remainder), all of which come from human life.
The basis of combinatorial counting is set operation. Probability theory was born from gambling, and set also plays a leading role in probability calculation. Mathematicians use sets to define natural numbers, which is beautiful.
There is a strong evidence that sets were not created by mathematicians, and that is the once mathematical crisis-the paradox of sets (limited space).
If mathematicians create the concept of set in order to achieve their own goals, then they must define the set, which is a recognized procedure for mathematicians.
But there is no definition of set so far, and because of this, mathematicians have long been dissatisfied with the concept of set and tried to make a clear definition.
Guess what the result is? The wolf came and found the paradox of set. At that time, many mathematicians were extremely pessimistic and thought that the mathematics building was going to collapse.
Because many mathematical concepts are defined by sets, and sets are contradictory, isn't the whole mathematics just punching yourself in the mouth?
At that time, there was a panic in the field of mathematics, and some unconvinced mathematicians tried their best to mend it after it was too late and put forward various rectification plans. This was at least the spirit of Ah Q.
Coincidentally, the mathematician Godel discovered the incomplete theorem, which gave a blow to the mathematicians who still had illusions and sentenced the perfectionist to death.
It was really a rainy day, and mathematics didn't recover until the beginning of last century. It turns out that the math building is really shabby, so it will be fine.
I tell this historical story only to prove that the collection is not easy to mess with. Mathematicians used it to build houses, and the result was greatly weakened. Therefore, the collection is by no means something they created from the remnants.
As for what problems can be solved by sets, just like what problems can be solved by numbers, it is countless.
Counting is like a gentle girl, she can be as good as she wants, never causing trouble, with countless ways and infinite charm.
Getting together is like a naughty boy. He has the ability to handle anything. Whoever annoys him will embarrass him.
Please spit if you are interested.