Nikolai, I read the article halfway, but still ... There are two apples in front of me (fact). Further, I, like a "sorcerer", multiply them by zero and still see two apples in front of me! Although, according to the laws of arithmetic, they should have disappeared from me! What does mathematics say about this? Thanks for the answer.
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| Two apples |
Here they are, beauties. They lie down and smile. Like, well, what do you say to that? So what is multiplication by zero? Let's try to figure this out.
Pay attention, the question is formulated very cleverly: not "what do mathematicians say?", but "what does mathematics say?". The first question is the easiest to answer. Preachers say, "Read the Bible," mathematicians say, "Read the Definition." They answer stupidly. Nobody needs to explain anything. And the meticulous can always, with a smart look, hang noodles on their ears.
Next, we will consider the situation from the position of the "sorcerer". The sorcerer declares that he will multiply the apples by zero. Then the sorcerer says: "Close your eyes and do not open." While your eyes are closed, the sorcerer hides the apples. "Open your eyes. See the apples? They are not there. The great miracle of multiplication by zero has happened - the apples have disappeared!" The sorcerer-mathematician will surely add: "What was required to be proved."
Now a few words about mathematicians. They, like proud eagles, soar high in the clouds of their abstract ideas. Mathematicians descend to our sinful earth only when they see food - a problem that they can solve. Mathematicians have learned very well to tear numbers from reality and perform various manipulations with them. When it becomes necessary to bring numbers back to reality, sometimes very big problems arise. Multiplying by zero is one such problem.
Let's start from the very beginning. The Russian-language Wikipedia page in one of the versions wrote: "Multiplication is one of the main binary mathematical operations (arithmetic operations) of two arguments (multiplicand and multiplier), the result of which is a new number (product). ... Multiplication by zero (zero element) gives a number equal to zero: x ⋅ 0 = 0".
If we translate the above quote into ordinary human language, then two elements (multiplicand and multiplier) are needed for multiplication. After multiplying them, a new element will be obtained, which is the result of multiplication. It is customary to write it like this:
a*b=c
On the left side of the equal sign is written what precedes the multiplication. The result of the multiplication is written on the right side. One element is multiplied by another element, resulting in a third element.
If we consider the logic of mathematicians, then calling zero the "zero element", all the "laws" of multiplication are observed - when multiplied by the zero element, all other elements turn into the zero element. There is only one question left: "Where do the apples go?".
Now I will present my own view on the problem of multiplication by zero. First read my reasoning, and at the end I will give practical recommendations on how to use my new knowledge. So what does the math say about multiplying by zero?
From the point of view of mathematics, multiplication by zero is impossible, since the multiplication itself does not occur. If in my earlier works I stated something else, then I was mistaken. The process of cognition is continuous and what seemed right to me yesterday may look completely different today.
The positional notation of numbers looks like this: units, tens, hundreds... If there is a number in the positional notation, then we write it down. For example, 324 is three hundred, two tens, four ones. And if there is no number in a separate position? What then? We write zero instead of the number that is missing. For example, 304 is three hundred, no tens, four units. I affirm that the absence of a number cannot be a number. In other words, zero is not a number and the rules of numbers do not apply to it.
In the multiplication example, zero represents an empty space in the place of one of the factors and an empty space in the result of the multiplication. Multiplication, as a mathematical operation, does not occur. It's like trying to clap with one hand. To get sound, there must be two palms. You see how smart we have become: we have determined that clapping is a binary operation that can be described by the mathematical operation of multiplication:
[one palm]*[other palm]=[applause]
Do you want to add numbers here? Please:
1[palm]*1[palm]=1[applause]
Now let's remove one palm. In our mathematical expression, we will replace one of the palms with zero and look at the result.
0[palm]*1[palm]=0[applause]
1[palm]*0[palm]=0[applause]
In order for the multiplication to occur, we need two completely different palms, and not the same one. Mathematicians tell us that when a number is raised to the second power, it multiplies itself. It is just as impossible to multiply a number by itself as it is impossible to create an applause with one palm.
You can say that in audio equipment, one speaker can produce sound, the second speaker is not needed for this. In the case of a speaker, there is another multiplication formula: the speaker is multiplied by the electric current and the result of the multiplication is sound.
1[speaker]*1[electric current]=1[sound]
If there is no speaker (for example, it is broken), the electric current cannot produce sound.
0[speaker]*1[electric current]=0[sound]
If there is no electric current (Putin cut off the wires), the speaker cannot produce sound.
1[speaker]*0[electric current]=0[sound]
In ordinary human language, the operation of multiplication by zero can be translated as follows:
0*b=0
Multiplication does not occur because there is nothing to multiply, the result of multiplication is absent.
a*0=0
Multiplication does not occur because there is nothing to multiply by, the result of multiplication is absent.
Something like this. Next time I will tell you about the zero element in multiplication.
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