What can you add to the name of our magazine?

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WHAT CAN BE ADDED TO THE TITLE
OF OUR MAGAZINE?

(REPLICA MATHEMATICS)

From the article “The History of Quantum,” written in the first issue of the magazine, the reader learned about the important concept of modern physics and the origin of the term “quantum.”
It is interesting to note that another term, this time a mathematical one, owes its origin to this gelatinous root. So the answer to the question posed in the title is not difficult for a mathematician.

Fig. 1

The term “quantifier” belongs to one of the most important branches of modern mathematics—mathematical logic—and entered scientific circulation at approximately the same time as “quantum,” i.e., at the beginning of our century.

Let us try to briefly explain the meaning of this term and the designations associated with it. Consider, for example, the following equality:

$$x^2 = 2^x.$$

(1)

and we will assign to the variable $x$ all possible natural numbers as values: 1, 2, 3, 4, 5, etc. It will turn out that for some natural values ​​$x$ equality (1) will be correct (true), and for others it will be incorrect (false). Thus, the equality $1^2 = 2^1$ is false, and the equality $4^2 = 2^4$ is true.

In connection with our initial equality, it is appropriate to consider two statements: 1) these equality are satisfied by this and (any) natural values ​​$x$, 2) there are natural values ​​$x$ that satisfy this equality.

Statement 1) is denoted in mathematical logic as follows:

$$\forall x (x^2 = 2^x).$$

The symbol $\forall$ is readable for everyone and is called a general quantifier. And this symbol comes from the English word All (which means everything), in which only the first letter was left (mathematicians are very economical), and then also turned over (mathematicians, scales, are inventive).

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For statement 2) the following notation is accepted:
$$\exists x (x^2 = 2^x).$$

The symbol $\exists$ is read by an existent and is called an existential quantifier. The origin of this symbol is similar: the English word Exist (which means to exist) was treated in the same way as the word All.

Telery, in the new abbreviated notation, we get
$$\forall x (x^2 = 2^x) = JI \quad (\text{ложь}),$$
$$\exists x (x^2 = 2^x) = H \quad (\text{истина}).$$

Let’s look at another example, in which the initial set will be the set of all adult people - thus, in the statements below, we resolve together $x$ “substitute” any adult. In this case, it is not without embarrassment to admit that the statement $\forall x (x - \text{честный человек})$ false, but this is somewhat reassuring about the truth of the statement $\exists x (x - \text{честный человек}).$

That’s all that can be said in the first case.

The origin of the term quantifier (the Latin word quatim means “how much” (connected to the fact that in traditional logic statements are classified according to “quantitative content” - according to how many objects they relate to. For example, “Petrov is an honest man” is a single narrowing. \exists x, x - \text{честный человек}} — частное сужение. «\forall x, x - \text{an honest man}} is a universal narrowing.

F. Leonidov