Mathematicians call a set a collection of elements united by a certain characteristic, a certain rule, and the number of elements in a given set is called the cardinality of that set. Let A be the set of natural numbers less than 5; then A = {1, 2, 3, 4}, and the cardinality of set A: |A| = 4, that is, A contains four elements, four numbers. There are sets that have an infinite number of elements, and they are divided into two types: countable and uncountable. Countable sets are those whose elements can be numbered: the first element, the second, the third, and so on. That is, all of them can be identified, an algorithm for finding them can be specified, and they can be ordered. For example, countable sets include: the set of natural numbers N = {1, 2, 3,…}, the set of all rational numbers Q = {m/n, where m and n are integers: e.g., 1/4, – 4/7, 11/3…}. All countable sets are equinumerous, and their cardinality equals (by definition) the cardinality of the set of natural numbers (|Q| = |N|). Uncountable sets are sets whose elements cannot be numbered, identified, ordered, for example, the set of all real numbers, the set of all irrational numbers. The cardinality of uncountable sets is called the continuum. Now let’s give an example-analogy.
Let’s take a Cartesian coordinate system. Mathematicians assert that the cardinality of the set of points of the segment (0, 1) (all real numbers on the segment (0, 1) – equal to the continuum) is equinumerous with the set of points of a square with side (0,1)1, equinumerous with the set of points of a cube with side (0,1)2 and so on. At first glance, it seems (obviously) that this assertion about the equinumerousness of the segment to the square, cube… – is complete nonsense. It is clear – well, it is obvious – that there are fewer points on the segment than on the square (the length of whose side is the same as the length of the segment) or in the cube! It is so obvious! But reality is actually quite different – they are indeed equinumerous, that is, they have the same number of points, elements. This is proven very simply. It is enough to show the correspondence of each element of one set to an element of another (to indicate the rule by which one element of one set will unambiguously correspond to an element of another set, that is, one element of one set cannot correspond to two different elements of another set; this is called constructing a function (rule), which has a function inverse to itself).
Let’s show the equinumerousness of the segment and the square: |(0,1)| = |(0,1) × (0,1)|. We will construct a rule-correspondence. All points of the segment (0,1) can be written in the form of a decimal number: a = 0,a1a2a3…an…, where a1, a2, a3, …, an are natural numbers (e.g., 0.1563986…). Each point of the square in the rectangular Cartesian coordinate system can be written in the form of a pair of numbers: (b, c) (where b, c are the coordinates of the point of the square on the coordinate axes), where b and c belong to the segment (0,1) and can be presented in the form: b = 0,b1b2b3…bn… and c = 0,c1c2c3…cn… And the rule that will match each point of the square, that is, each pair of numbers (b, c) = (0,b1b2b3…, 0,c1c2c3…) will correspond to a point from the segment (0,1), chosen as follows: a = 0,b1c1b2c2b3c3…bncn… According to this rule, each other point of the square (each pair of numbers (b, c)) will correspond to another point from the segment! The inverse rule to this will correspond to each point of the segment a point of the square: a = 0,a1a2a3…an…, which will correspond to a point with coordinates (b, c) = (0,a1a3a5…a2n-1…, 0,a2a4a6…a2n…). So, two different points of the square correspond to two different points of the segment, and with the inverse function – two different points of the segment correspond to two different points of the square. Therefore, the number of points of the segment (0,1) is the same as the number of points of the square (0,1) × (0,1). Similarly, we prove the equinumerousness of the segment and the cube of n-dimensional space: |(0,1)| = |(0,1)n|. When this fact was seen by the patriarchs of set theory, many of them ended up in psychiatric hospitals, went insane. They said: I see, but I do not believe! I see, – because the proof clearly shows their equinumerousness, but I do not believe, – because it is obvious that there are many more points on the square or in the cube than on the segment!? If even in mathematics a change of mind is necessary, a change of thinking style (otherwise the psychiatric hospital awaits such a poor scientist), then even more so it is necessary to change stereotypes of thinking when we touch the created mind to the Heavenly, Hypostatic things!
So, a Christian = the fullness of the Holy Spirit, a parish = the fullness of the Holy Spirit, a patriarchate = the fullness of the Holy Spirit, all Christians = the fullness of the Holy Spirit! The Church is the fullness of the Holy Spirit! “I in You, and You in Me, We in them, and they in Us!” Whoever has ears to hear, let them understand!