Suppose we have a set of

**A**, consisting of four people. This set is formed on the basis of "people." We denote the elements of this set by the letter

**"a"**, the subscript with a number will indicate the serial number of each person in this set. We introduce a new unit of measurement "gender" and denote it with the letter

**"b"**. Since sexual characteristics are common to all people, we multiply each element of the set

**A**by sexual characteristic

**b**. Please note that now our multitude of “people” has turned into a multitude of “people with sexual characteristics”. After that, we can divide the sexual characteristics into male

**bm**and female

**bw**sexual characteristics. Now we can apply the mathematical filter: we choose one of these sexual characteristics, no matter which one - male or female. If it is present in a person, then we multiply it by one; if there is no such sign, we multiply it by zero. And then we use ordinary school math. See what happened.

Set and subset |

After multiplication, contractions, and rearrangements, we got two subsets: a subset of Bm men and a subset of Bw women. Mathematicians reason the same way when they apply set theory in practice. But they don’t dedicate us in detail, but give the finished result - "a set of people consist of a subset of men and a subset of women." Naturally, you may wonder how correctly mathematics is applied in the above transformations? I dare to assure you that, in essence, everything was done correctly; it’s enough to know the mathematical justification of arithmetic, Boolean algebra and other branches of mathematics. What it is? Some other time, I'll tell you about it.

You can combine two sets into one by selecting the unit of measure present in the elements of these two sets.

As you can see, units of measure and ordinary mathematics turn set theory into a relic of the past. A sign that the set theory is not all right is that for set theory mathematicians have come up with their own language and their own notation. Mathematicians did what shamans once did. Only shamans know how to "apply" their "knowledge" correctly. They teach us this "knowledge".

In conclusion, I want to show you how mathematicians manipulate infinite sets.