Breaking "matches" or "Breaking" matches
“During the six months of my time at the institute, they gave Aldan only one task, which all went down to the same division of zero by zero and did not contain any absolute truth. Maybe one of them was engaged in the real business, but I did not know anything about it. „
Arkady and Boris Strugatsky. Monday begins on Saturday
Substitution of concepts is one of the foundations of a good puzzle. Most often for this is used allegorical or humorous story. For example, in a puzzle it is asked “Vasya had three apples; he lost one; how many apples did Vasya have left? ”In the end, it turns out that the apples were quantum (this is obvious to all normal puzzle lovers) and the apple was not lost, but simply when Vasya tried to count the number of apples according to the principle of uncertainty, he now cannot determine it location, although he knows for sure that he had one apple.
Honestly, there is nothing wrong with such a presentation, especially when it comes to a fairly narrow circle of puzzle lovers and subscribers of the Kvant library. But sometimes such liberty touches and directly mathematical axioms.
')
Let us once again turn to the problem of the damage of matches, which has already given birth to two okolomathematicheskikh holivara - "Breaking matches ..." and "On Lebesgue's criterion ..."
Strictly speaking, the same dream is, on the one hand, funny mathematical exercises and fan, on the other hand, the violation of truths.
First, those who wish can familiarize themselves with the concept of probability on the Wikipedia website Probability ;
Secondly, it should be understood that at a point, on a segment, on a straight line, on a plane, in a multidimensional space, no events can occur except those that are the result of mathematical laws in the form of functions. That is, the segment can not be "broken", and it can not be painted, weighed, put in a pawnshop or put in a corner.
Absolutely illegal is the statement "Let's randomly intersect the circle of a line." This is not yet possible to do. Because in the mathematics there are no functions that could return random values.
All space in mathematics is strictly defined at the moment. A person who comes up with a random mathematical function will be the greatest mathematician of all times and peoples.
What follows from all this? Are topic authors right when taking limits at a point in terms of a non-existent function? I would not like to give unambiguous assessments. As a matter of fact, I am writing a post instead of responding to a comment just to show the following:
With mathematical abstractions only mathematics can “happen”. For example, one segment either intersects another or not. He cannot cross it with some probability;
The point - does not exist and therefore the question of the probability of a non-existent event in a non-existent place looks strange even to mathematicians;
And most importantly, the authors took the Probability as a basis for their topics, although they could just as well take the Mass, the Dollar Rate, the Rules of the Road and calculate the limit of these functions at a point. The answer would be the same 0. Although in my opinion the answer should be so NULL.
I strongly advise the authors of topics and everyone to try to answer the following questions:
- What is the probability that the “match” will “break” at one of its ends?
- What is the probability that the circle drawn from the end of the segment, whose diameter is equal to the length of the segment, intersects it in the middle?
- What is the probability that the parallel lines intersect?
At the same time, I am far from the idea that the authors made a mistake in calculating limits or integrals. Just wanted to say that the Integral of the cat on a closed loop does not exist, and is not zero.
upd
Or, to put it concretely, all measures of geometric objects are absolute and fully determined at the moment of their description.
Events can not occur in any geometry, and therefore the concept of probability does not apply to geometry.
Arkady and Boris Strugatsky. Monday begins on Saturday
Substitution of concepts is one of the foundations of a good puzzle. Most often for this is used allegorical or humorous story. For example, in a puzzle it is asked “Vasya had three apples; he lost one; how many apples did Vasya have left? ”In the end, it turns out that the apples were quantum (this is obvious to all normal puzzle lovers) and the apple was not lost, but simply when Vasya tried to count the number of apples according to the principle of uncertainty, he now cannot determine it location, although he knows for sure that he had one apple.
Honestly, there is nothing wrong with such a presentation, especially when it comes to a fairly narrow circle of puzzle lovers and subscribers of the Kvant library. But sometimes such liberty touches and directly mathematical axioms.
')
Let us once again turn to the problem of the damage of matches, which has already given birth to two okolomathematicheskikh holivara - "Breaking matches ..." and "On Lebesgue's criterion ..."
Strictly speaking, the same dream is, on the one hand, funny mathematical exercises and fan, on the other hand, the violation of truths.
First, those who wish can familiarize themselves with the concept of probability on the Wikipedia website Probability ;
Secondly, it should be understood that at a point, on a segment, on a straight line, on a plane, in a multidimensional space, no events can occur except those that are the result of mathematical laws in the form of functions. That is, the segment can not be "broken", and it can not be painted, weighed, put in a pawnshop or put in a corner.
Absolutely illegal is the statement "Let's randomly intersect the circle of a line." This is not yet possible to do. Because in the mathematics there are no functions that could return random values.
All space in mathematics is strictly defined at the moment. A person who comes up with a random mathematical function will be the greatest mathematician of all times and peoples.
What follows from all this? Are topic authors right when taking limits at a point in terms of a non-existent function? I would not like to give unambiguous assessments. As a matter of fact, I am writing a post instead of responding to a comment just to show the following:
With mathematical abstractions only mathematics can “happen”. For example, one segment either intersects another or not. He cannot cross it with some probability;
The point - does not exist and therefore the question of the probability of a non-existent event in a non-existent place looks strange even to mathematicians;
And most importantly, the authors took the Probability as a basis for their topics, although they could just as well take the Mass, the Dollar Rate, the Rules of the Road and calculate the limit of these functions at a point. The answer would be the same 0. Although in my opinion the answer should be so NULL.
I strongly advise the authors of topics and everyone to try to answer the following questions:
- What is the probability that the “match” will “break” at one of its ends?
- What is the probability that the circle drawn from the end of the segment, whose diameter is equal to the length of the segment, intersects it in the middle?
- What is the probability that the parallel lines intersect?
At the same time, I am far from the idea that the authors made a mistake in calculating limits or integrals. Just wanted to say that the Integral of the cat on a closed loop does not exist, and is not zero.
upd
Or, to put it concretely, all measures of geometric objects are absolute and fully determined at the moment of their description.
Events can not occur in any geometry, and therefore the concept of probability does not apply to geometry.
Source: https://habr.com/ru/post/167317/
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