For example, recall the trial of the Lord Jesus Christ: how the Lord stood (in the full height of Humanity, full of Divine Meekness and Humility) before Herod (in silence, full of love-mercy), Pilate (talking about the Kingdom of God and Truth), on the Sanhedrin (remember at least the episode when a servant hit the Lord in the face and how the Lord talked to him and helped this servant rise at least to the level of reason, logic, responsibility: “If I said something wrong, testify as to what is wrong. But if I spoke the truth, why did you strike me?”), before the soldiers who mocked Him, jeered at Him, – did not threaten anyone, did not get angry, did not judge and was not a victim!!! The aggressor (aggressor-initiator (who initiates aggression) and aggressor-reactor (who responds with aggression to aggression)) and the crawler (one who is in the state of offended, a victim: guilty or innocent, it does not matter) – these are two sides of the same hellish medal – pride. Aggression (and aggressive self-devouring, gnawing, reacting to aggression) is a manifestation (symptom) of pride, just as crawling (victim position), baseness (no less than aggression) is a manifestation of pride!!! Humility is to stand (walk, act, speak, be) in the full height of human dignity (greatness, vocation – to be children of the Heavenly Father, gods by Grace). A person’s behavior is always a manifestation of inner content-spirit (discern what spirit you are: if you are aggressive or offended, poor victims – this is a manifestation of the spirit of pride, blindness-delusion, mindlessness; watch yourself, because often what people (“Orthodox”) consider humility (high) is extreme pride (abominable before God))!
We have already discussed working with infinities and sets with the power of the continuum requires a changed mindset – see Part III. Many have gone mad when faced with such facts (properties of non-contradictory infinity): I see that AO > CO by the magnitude of AC, but the proof unequivocally shows that AO = CO (because AC + ∞ = ∞). To comprehend and accept this, there must be repentance, a change of mind, otherwise – madness, “the roof will go off.”
Now, finally, let’s solve our equation:
It is clear that solving it “head-on,” that is, eliminating the radicals (square roots) by squaring both sides, will not yield anything useful – we will get after such a transformation an even harder equation:
So, directly eliminating the irrationality here is too cumbersome, as they say, from one extreme to another. But there is an alternative maneuver. Let’s make the following transformation: under the square root in the fiftieth radical, instead of 3.97, substitute the entire expression with fifty radicals (the left side of the equality), which is equal (identical) to 3.97 and get:
where there are already one hundred radicals. You say: instead of simplifying the problem, you have made it more complicated: there were 50 radicals, and now there are 100?! Why? – You will understand in a moment. Now in the hundredth radical, instead of 3.97, again substitute 50 radicals (or 100). And so, we continue this procedure to infinity! As a result of such transformations, we get:
(where there are radicals – an infinite number of them, and this radical (or the number 3.97) is not visible at all – it is very far, in infinity), so it is better to write like this:
Now, whichever radical you take (they all have the same value), it will be equal to 3.97 (remember the rays AO=BO=CO=DO). We illustrate this by marking the radicals with letters A, B, C, D, and the last radical (or the number 3.97 under the last radical) with the letter O.
After such elementary reasoning (from the point of view of infinity), we can now proceed to solving with a finite number of radicals, substituting in AO the radical BO (we get the equation:
or CO
or DO
All these equations are identical, so we choose (and solve) the one that is easiest (orally) to solve, namely:
Square both sides:
Thus, understanding the principle (focus with infinity) of solving this equation (we will further explain this principle with an example from physics (but not chewing it over as for toothless grandmothers, but considering it briefly)), you can jokingly explain (retell) it to your colleagues in the workshop (biologist – to biologists, chemist – to chemists, shepherd – to shepherds, cattle breeder – to cattle breeders, fraudster-thief – to fraudsters-thieves, etc.) in the language familiar to them, scientifically-professionally-everyday… But if you cannot come up with such an example-parable (that is, you did not understand what it is about – although it is impossible, because Dzyunyo understood), then write to the elder and order… let him invent for you, so that you have something to “shine” (with mind) before colleagues, friends… Although the parable is not for “shining” or boasting – but for repentance-humility!!!
So, understanding the principle of elementary transformations and the properties of infinity, let’s continue with another example to illustrate the same concept in a different context, such as physics.