Set and multiset

The concepts of “set” and “multiset” are two trump ace in the sleeves of a sharpie, one in each sleeve. The sharpie takes out from the sleeve that trump ace, which is more convenient for him to get. In any case, the sharpie always wins. In the same way, any mathematician will always justify set theory.

There can’t be two identical elements in a set, but if there are identical elements in a set, such a set is called a “multiset.” Intelligent beings can never understand such a logic of absurdity. This is the level of talking parrots and trained monkeys. Mathematicians act as ordinary animal trainer, preaching to us their absurd ideas.

Once the engineers who built the bridge, during the testing of the bridge, were in a boat under the bridge. If the bridge collapsed, a mediocre engineer died under the rubble of his creation. If the bridge could withstand the load, a talented engineer built other bridges.

No matter how mathematicians hide behind the phrase “mathematics studies abstract concepts”, there is one umbilical cord that inextricably connects them with reality. This umbilical cord is money. We apply the mathematical set theory to the mathematicians themselves.

We studied mathematics very well and now we are giving out salaries. Here comes a mathematician for his money. We count the whole amount to him and lay out on his table on different piles, into which we place banknotes of the same denomination. Then we take one banknote from each pile and hand over to the mathematician his "mathematical set of salary." We explain the mathematics that he will receive the remaining bills only when he proves that a set without the same elements is not equal to a set with the same elements. After that, the most interesting will happen.

Set and multiset

First of all, the logic of the deputies will work: "It can be applied to others, but not to me!" Further, the mathematician will assure us that on banknotes of the same denomination there are different numbers of banknotes, therefore they cannot be considered the same elements of the set. Well, we count the salary in coins - there are no numbers on the coins. Here, the mathematician will frantically recall physics: different coins have different amounts of dirt, the crystal structure and arrangement of atoms of each coin is unique ...

And now I have the most interesting question: where is the line behind which the elements of the multiset turn into the elements of the set and vice versa? Such a facet does not exist - shamans decide everything, science is absent here.

You see that the same set of elements is both a multitude and a multiset at the same time. How right? And here the mathematician-shaman-schuller takes an ace from his sleeve and begins to tell us either about the multitude or the multiset. In any case, he will convince us that the theory of sets is correct.

To understand how modern shamans apply set theory to reality, it is enough to answer one question: how do the elements of one set differ from the elements of another set? I will show you how to do it.