or vice versa – saw
and replaced it (or drew) with “5” because
Let’s practice transforming expressions, replacing the corresponding elements with identical ones. For example,
– this means that wherever we see “7”, we can write “√” instead, and where we see “√” we can write “7”.
And by doing such substitutions to infinity (∞), we get:
more precisely, it can be written:
(and there (in ∞), very, very far beyond the horizon, it is not visible ☺)
Don’t be surprised that the elder chews such elementary principles for so long – our grandmothers are not very bright – the elder tries to explain something at the blackboard, to clarify, to convey, and they sit in class and nod off like hens on the perches or impatiently wait for the time of questions to ask the old man: “And you, when you go to bed, do you put your beard under the blanket or on top of it?” ☺. And to such grandmothers (and lazy Dzyunyo) the elder aims to teach at least some basic knowledge (of Heavenly) mathematics; and when he is told that the grandmothers are made this way, you will not succeed, do not waste your time – the elder does not give up, and replies: “they teach a bear to ride a bike, so won’t we teach our grandmothers the elementary, it can’t be – we will definitely teach!” (The elder has great faith in the person, in the image of God and his potential). And that rascal Dzyunyo constantly mocks the old man and grumbles under his breath at those grandmothers (although no better than them) and that old man: “wants to teach dumb chickens to soar like eagles – the old man has completely lost his mind…”. But the elder does not pay attention to those grumbles, and continues his work!).
Dzyunyo, after the old man explained the elementary transformation of mathematical expressions, said to the old man: “You are completely detached from reality, you better explain this principle of substituting identical expressions to those who nod off on the perches using the example of money: pension or change in the store – here at least there is a chance that the grandmothers will understand something!” (But do not think that Dzyunyo is so pious – he cares about others – he just did not understand anything himself, and knowing that the old man checks each one individually, so as not to appear completely ignorant, he pretends as if he cares about other classmates). It is not difficult for the elder to give examples from everyday life: be it a pension, or counting change at the store…
For example, the seller in the store should give you 10 hryvnias change and asks: “Do you want it in coins or notes?”. And you know very well that whether 10 UAH is in coins (by one kopeck, by 5 kopecks, by 10 kopecks, etc.) or paper (or part paper and part coins), the value of money is the same, but the form, volume, mass (of the banknotes or coins) is different. And you consider: in what form to take the change or pension, how convenient it will be to use that money in each specific situation (somewhere you need coins, and somewhere notes, and of the largest denomination possible); but, agree, to take a monthly pension by one kopeck is too much, although it is the same amount as in notes of 200 or 500 UAH. Therefore, we sometimes say: “please break 100 UAH into 10 UAH” or vice versa… We replace identical in essence, but different in form realities to achieve the most convenient result-goal. Understood? The elder explains until even Dzyunyo understands. And if even the lazy Dzyunyo understands (the proof or the logic of some reasoning, the logic of a method), and he studied only for two years: a year to walk and a year to talk (that is, he finished two grades and that online!?), then the elder moves on to explain new material, being sure that everyone understood (except, of course, those who dozed off the lesson, like chickens on the perches, but when they wake up, they will quickly understand the proof-logic themselves – because even Dzyunyo understood, meaning everyone can if they want). Therefore, the elder tests all the medicines-thoughts on Dzyunyo. If he understood – then everyone can understand (under the necessary conditions: the desire to know the truth, sincerity, impartiality, obedience!). And we also apologize to you for having to listen to such elementary explanations (childish analogies), but please do not forget that they are addressed to those who, when asked: “Which is heavier – a kilogram of iron or cotton?” with one hundred percent (100%) confidence answer: “It’s clear to a donkey that a kilogram of iron… iron is heavier than cotton!”. And to such children, the elder tries to explain the basics of mathematics (earthly, and in parables-analogies – Heavenly).
Understanding the principle of elementary transformations of mathematical expressions, let’s get acquainted with the next principle, which we will also use to solve our equation. Consider the segment AO, which is divided by points B, C, D into 10 segments (for the sake of illustration, we will consider only the segments AO, BO, CO, DO for the principle we need).