NUMBER e. A number approximately equal to 2.718, which is often found in mathematics and natural sciences. For example, when breaking radioactive substance after time t from the initial amount of the substance remains a fraction equal to e–kt, where k- a number characterizing the decay rate given substance. Reciprocal 1/ k is called the average lifetime of an atom of a given substance, since, on average, an atom, before decaying, exists for a time 1/ k. Value 0.693/ k is called the half-life of a radioactive substance, i.e. the time it takes for half of the original amount of the substance to decay; the number 0.693 is approximately equal to log e 2, i.e. base logarithm of 2 e. Similarly, if bacteria in a nutrient medium multiply at a rate proportional to their number in this moment, then after time t initial number of bacteria N turns into Ne kt. attenuation electric current I in a simple circuit with serial connection, resistance R and inductance L happens according to law I = I 0 e–kt, where k = R/L, I 0 - current strength at the time t= 0. Similar formulas describe stress relaxation in a viscous fluid and damping magnetic field. Number 1/ k often referred to as relaxation time. In statistics, the value e–kt occurs as the probability that over time t there were no events occurring randomly with an average frequency k events per unit of time. If a S- amount of money invested r interest with continuous accrual instead of accrual at discrete intervals, then by the time t the initial amount will increase to Setr/100.
The reason for the "omnipresence" of the number e is that the formulas mathematical analysis containing exponential functions or logarithms, are written easier if the logarithms are taken in base e, not 10 or some other base. For example, the derivative of log 10 x equals (1/ x)log 10 e, while the derivative of log ex is just 1/ x. Similarly, the derivative of 2 x equals 2 x log e 2, while the derivative of e x equals just ex. This means that the number e can be defined as the basis b, for which the graph of the function y= log b x has at the point x= 1 tangent to slope factor, equal to 1, or at which the curve y = bx has in x= 0 tangent with slope equal to 1. Base logarithms e are called "natural" and denoted by ln x. Sometimes they are also called "non-Perean", which is incorrect, since in reality J. Napier (1550–1617) invented logarithms with a different base: the non-Perian logarithm of a number x equals 10 7 log 1/ e (x/10 7) .
Various degree combinations e are so common in mathematics that they have special names. These are, for example, the hyperbolic functions
Function Graph y=ch x called a catenary; a heavy inextensible thread or chain suspended by the ends has such a shape. Euler formulas
where i 2 = -1, bind number e with trigonometry. special case x = p leads to the famous relation ip+ 1 = 0, linking the 5 most famous numbers in mathematics.
The number appeared relatively recently. It is sometimes called the "non-number" in honor of the Scottish mathematician John Napier (1550-1617), the inventor of logarithms, but is unfounded, since there is no firm basis for claiming that Napier had a number e clear representation" . For the first time notation " e"introduced by Leonhard Euler (1707-1783). He also calculated the exact 23 decimal places of this number using the number representation e in the form of an endless number series: received by Daniel Bernoulli (1700-1782). "In 1873 Hermite proved the transcendence of the number e.L Euler got a remarkable result relating the numbers e, p, and: . He also has the merit of defining a function for complex values z, which marked the beginning of mathematical analysis in the complex field - the theory of functions of a complex variable ". Euler obtained the following formulas: Consider logarithms in base e, called natural and denoted Lnx.
Methods for determining
Number e can be defined in several ways.
Through the limit:
(second wonderful limit) .
As the sum of the series:
how singular a, for which
Like the only positive number a, for which is true
Properties
This property plays important role in solving differential equations. For example, the only solution differential equation is a function where c is an arbitrary constant.
Number e irrational and even transcendental. This is the first number that was not specifically deduced as transcendent; its transcendence was proved only in 1873 by Charles Hermite. It is assumed that e- a normal number, that is, the probability of the appearance of different digits in its record is the same.
See Euler's formula in particular
Another formula that connects numbers e and R, so-called "Poisson integral" or "Gauss integral"
For anyone complex number z the following equalities are true:
Number e expands into an infinite continued fraction as follows:
Presentation of Catalan:
Story
This number is sometimes called non-Perov in honor of the Scottish scientist Napier, author of the work "Description of the amazing table of logarithms" (1614). However, this name is not entirely correct, since it has the logarithm of the number x was equal
For the first time, the constant is tacitly present in the appendix to the translation into English language the aforementioned work by Napier, published in 1618. Behind the scenes, because it contains only a table of natural logarithms determined from kinematic considerations, the constant itself is not present (see: Napier).
The very same constant was first calculated by the Swiss mathematician Bernoulli when analyzing the following limit:
The first known use of this constant, where it was denoted by the letter b, found in Leibniz's letters to Huygens, 1690-1691.
letter e Euler began using it in 1727, and the first publication with this letter was his work "Mechanics, or the Science of Motion, Stated Analytically" in 1736. Respectively, e commonly called Euler number. Although later some scholars used the letter c, letter e used more often and is now the standard designation.
Why was the letter chosen? e, is not exactly known. Perhaps this is due to the fact that the word begins with it exponential("exponential", "exponential"). Another assumption is that the letters a, b, c and d already widely used for other purposes, and e was the first "free" letter. It is implausible that Euler chose e as the first letter of your last name Euler) [source not specified 334 days] .
e- mathematical constant, base natural logarithm, an irrational and transcendental number. e= 2.718281828459045… Sometimes a number e called Euler number or non-peer number. Plays an important role in differential and integral calculus.
Methods for determining
The number e can be defined in several ways.
Properties
Story
This number is sometimes called non-Perov in honor of the Scottish scientist John Napier, author of the work "Description of the amazing table of logarithms" (1614). However, this name is not entirely correct, because it has the logarithm of the number x was equal 
.
For the first time, the constant is tacitly present in the appendix to the English translation of the aforementioned Napier's work, published in 1618. Behind the scenes, because it contains only a table of natural logarithms, the constant itself is not defined. It is assumed that the author of the table was the English mathematician William Oughtred. The very same constant was first deduced by the Swiss mathematician Jacob Bernoulli when trying to calculate the value of the following limit:
The first known use of this constant, where it was denoted by the letter b, found in letters from Gottfried Leibniz to Christian Huygens, 1690 and 1691. letter e began to be used by Leonhard Euler in 1727, and the first publication with this letter was his work "Mechanics, or the Science of Motion, Stated Analytically" in 1736. Accordingly, e sometimes called Euler number. Although later some scholars used the letter c, letter e used more often and is now the standard designation.
Why was the letter chosen? e, is not exactly known. Perhaps this is due to the fact that the word begins with it exponential("exponential", "exponential"). Another assumption is that the letters a,b,c and d already widely used for other purposes, and e was the first "free" letter. It is implausible that Euler chose e as the first letter of your last name Euler), because he was a very modest person and always tried to emphasize the importance of the work of other people.
Memorization methods
Number e can be remembered according to the following mnemonic rule: two and seven, then two times the year of birth of Leo Tolstoy (1828), then the angles of an isosceles right triangle ( 45 ,90 and 45 degrees).
In another version of the rule e associated with US President Andrew Jackson: 2 - so many times elected, 7 - he was the seventh president of the United States, 1828 - the year of his election, repeated twice, since Jackson was elected twice. Then - again, an isosceles right triangle.
In another interesting way, it is proposed to remember the number e with an accuracy of three decimal places through the "number of the devil": you need to divide 666 by a number made up of the numbers 6 - 4, 6 - 2, 6 - 1 (three sixes, of which reverse order the first three powers of two are removed): 
.
In the fourth method, it is proposed to remember e as 
.
A rough (with an accuracy of 0.001), but a beautiful approximation assumes e equal. A very rough (with an accuracy of 0.01) approximation is given by the expression.
"Boeing Rule": gives a good accuracy of 0.0005.
"Verse": We fluttered and shone, but got stuck in the pass; did not recognize our stolen rally.
e = 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69995 95749 66967 62772 40766 30353 54759 45713 82178 52516 64274 27466 39193 20030 59921 81741 35966 29043 57290 03342 95260 59563 07381 32328 62794 34907 63233 82988 07531 95251 01901 15738 34187 93070 21540 89149 93488 41675 09244 76146 06680 82264 80016 84774 11853 74234 54424 37107 53907 77449 92069 55170 27618 38606 26133 13845 83000 75204 49338 26560 29760 67371 13200 70932 87091 27443 74704 72306 96977 20931 01416 92836 81902 55151 08657 46377 21112 52389 78442 50569 53696 77078 54499 69967 94686 44549 05987 93163 68892 30098 79312 77361 78215 42499 92295 76351 48220 82698 95193 66803 31825 28869 39849 64651 05820 93923 98294 88793 32036 25094 43117 30123 81970 68416 14039 70198 37679 32068 32823 76464 80429 53118 02328 78250 98194 55815 30175 67173 61332 06981 12509 96181 88159 30416 90351 59888 85193 45807 27386 67385 89422 87922 84998 92086 80582 57492 79610 48419 84443 63463 24496 84875 60233 62482 70419 78623 2090 0 21609 90235 30436 99418 49146 31409 34317 38143 64054 62531 52096 18369 08887 07016 76839 64243 78140 59271 45635 49061 30310 72085 10383 75051 01157 47704 17189 86106 87396 96552 12671 54688 95703 50354 02123 40784 98193 34321 06817 01210 05627 88023 51920
In the fifth century BC, the ancient Greek philosopher Zeno of Elea formulated his famous aporias, the most famous of which is the aporia "Achilles and the tortoise". Here's how it sounds:Let's say Achilles runs ten times faster than the tortoise and is a thousand paces behind it. During the time during which Achilles runs this distance, the tortoise crawls a hundred steps in the same direction. When Achilles has run a hundred steps, the tortoise will crawl another ten steps, and so on. The process will continue indefinitely, Achilles will never catch up with the tortoise.
This reasoning became a logical shock for all subsequent generations. Aristotle, Diogenes, Kant, Hegel, Gilbert... All of them, in one way or another, considered Zeno's aporias. The shock was so strong that " ... discussions continue at the present time, to come to a common opinion about the essence of paradoxes scientific community has not yet succeeded ... mathematical analysis, set theory, new physical and philosophical approaches; none of them became a universally accepted solution to the problem ..."[Wikipedia," Zeno's Aporias "]. Everyone understands that they are being fooled, but no one understands what the deception is.
From the point of view of mathematics, Zeno in his aporia clearly demonstrated the transition from the value to. This transition implies applying instead of constants. As far as I understand, the mathematical apparatus for applying variable units of measurement has either not yet been developed, or it has not been applied to Zeno's aporia. The application of our usual logic leads us into a trap. We, by the inertia of thinking, apply constant units of time to the reciprocal. With physical point To the eye, it looks like time slowing down until it stops completely at the moment when Achilles catches up with the tortoise. If time stops, Achilles can no longer overtake the tortoise.
If we turn the logic we are used to, everything falls into place. Achilles runs with constant speed. Each subsequent segment of its path is ten times shorter than the previous one. Accordingly, the time spent on overcoming it is ten times less than the previous one. If we apply the concept of "infinity" in this situation, then it would be correct to say "Achilles will infinitely quickly overtake the tortoise."
How to avoid this logical trap? Remain in constant units of time and do not switch to reciprocals. In Zeno's language, it looks like this:
In the time it takes Achilles to run a thousand steps, the tortoise crawls a hundred steps in the same direction. For the next time interval, equal to the first, Achilles will run another thousand steps, and the tortoise will crawl a hundred steps. Now Achilles is eight hundred paces ahead of the tortoise.
This approach adequately describes reality without any logical paradoxes. But it is not complete solution Problems. Einstein's statement about the insurmountability of the speed of light is very similar to Zeno's aporia "Achilles and the tortoise". We have yet to study, rethink and solve this problem. And the solution must be sought not in infinitely large numbers, but in units of measurement.
Another interesting aporia of Zeno tells of a flying arrow:
A flying arrow is motionless, since at each moment of time it is at rest, and since it is at rest at every moment of time, it is always at rest.
In this aporia logical paradox it is overcome very simply - it is enough to clarify that at each moment of time the flying arrow rests at different points in space, which, in fact, is movement. There is another point to be noted here. From one photograph of a car on the road, it is impossible to determine either the fact of its movement or the distance to it. To determine the fact of the movement of the car, two photographs taken from the same point at different points in time are needed, but they cannot be used to determine the distance. To determine the distance to the car, you need two photographs taken from different points space at one point in time, but it is impossible to determine the fact of movement from them (naturally, additional data for calculations are still needed, trigonometry will help you). What do I want to focus on Special attention, is that two points in time and two points in space are different things that should not be confused, because they provide different opportunities for exploration.
Wednesday, July 4, 2018
Very well the differences between set and multiset are described in Wikipedia. We look.
As you can see, "the set cannot have two identical elements", but if there are identical elements in the set, such a set is called a "multiset". Reasonable beings will never understand such logic of absurdity. This is the level of talking parrots and trained monkeys, in which the mind is absent from the word "completely." Mathematicians act as ordinary trainers, preaching their absurd ideas to us.
Once upon a time, the engineers who built the bridge were in a boat under the bridge during the tests of the bridge. If the bridge collapsed, the mediocre engineer died under the rubble of his creation. If the bridge could withstand the load, the talented engineer built other bridges.
No matter how mathematicians hide behind the phrase "mind me, I'm in the house", or rather "mathematics studies abstract concepts", there is one umbilical cord that inextricably connects them with reality. This umbilical cord is money. Applicable mathematical theory sets to the mathematicians themselves.
We studied mathematics very well and now we are sitting at the cash desk, paying salaries. Here a mathematician comes to us for his money. We count the entire amount to him and lay it out on our table into different piles, in which we put bills of the same denomination. Then we take one bill from each pile and hand it to the math " mathematical set We explain the mathematics that he will receive the rest of the banknotes only when he proves that the set without identical elements is not equal to the set with the same elements. This is where the fun begins.
First of all, the deputies' logic will work: "you can apply it to others, but not to me!" Further, assurances will begin that there are different banknote numbers on banknotes of the same denomination, which means that they cannot be considered identical elements. Well, we count the salary in coins - there are no numbers on the coins. Here the mathematician will begin to convulsively recall physics: on different coins there is different amount dirt, crystal structure and atomic arrangement of each coin is unique...
And now I have the most interest Ask: where is the boundary beyond which elements of a multiset turn into elements of a set and vice versa? Such a line does not exist - everything is decided by shamans, science here is not even close.
Look here. We select football stadiums with the same area fields. The area of the fields is the same, which means we have a multiset. But if we consider the names of the same stadiums, we get a lot, because the names are different. As you can see, the same set of elements is both a set and a multiset at the same time. How right? And here the mathematician-shaman-shuller takes out a trump ace from his sleeve and begins to tell us either about a set or a multiset. In any case, he will convince us that he is right.
To understand how modern shamans operate with set theory, tying it to reality, it is enough to answer one question: how do the elements of one set differ from the elements of another set? I will show you, without any "conceivable as not a single whole" or "not conceivable as a single whole."
Sunday, March 18, 2018
The sum of the digits of a number is a dance of shamans with a tambourine, which has nothing to do with mathematics. Yes, in mathematics lessons we are taught to find the sum of the digits of a number and use it, but they are shamans for that, to teach their descendants their skills and wisdom, otherwise shamans will simply die out.
Do you need proof? Open Wikipedia and try to find the "Sum of Digits of a Number" page. She doesn't exist. There is no formula in mathematics by which you can find the sum of the digits of any number. After all, numbers are graphic symbols, with the help of which we write numbers and in the language of mathematics the task sounds like this: "Find the sum of graphic symbols representing any number." Mathematicians cannot solve this problem, but shamans can do it elementarily.
Let's figure out what and how we do in order to find the sum of the digits of a given number. And so, let's say we have the number 12345. What needs to be done in order to find the sum of the digits of this number? Let's consider all the steps in order.
1. Write down the number on a piece of paper. What have we done? We have converted the number to a number graphic symbol. This is not a mathematical operation.
2. We cut one received picture into several pictures containing separate numbers. Cutting a picture is not a mathematical operation.
3. Convert individual graphic characters to numbers. This is not a mathematical operation.
4. Add up the resulting numbers. Now that's mathematics.
The sum of the digits of the number 12345 is 15. These are the "cutting and sewing courses" from shamans used by mathematicians. But that is not all.
From the point of view of mathematics, it does not matter in which number system we write the number. So, in different systems reckoning, the sum of the digits of the same number will be different. In mathematics, the number system is indicated as a subscript to the right of the number. With a large number 12345 I don’t want to fool my head, consider the number 26 from the article about. Let's write this number in binary, octal, decimal and hexadecimal number systems. We will not consider each step under a microscope, we have already done that. Let's look at the result.
As you can see, in different number systems, the sum of the digits of the same number is different. Similar result has nothing to do with mathematics. It's like finding the area of a rectangle in meters and centimeters would give you completely different results.
Zero in all number systems looks the same and has no sum of digits. This is another argument in favor of the fact that . A question for mathematicians: how is it denoted in mathematics that which is not a number? What, for mathematicians, nothing but numbers exists? For shamans, I can allow this, but for scientists, no. Reality is not just about numbers.
The result obtained should be considered as proof that number systems are units of measurement of numbers. Because we can't compare numbers with different units measurements. If the same actions with different units of measurement of the same quantity lead to different results after comparing them, then this has nothing to do with mathematics.
What is real mathematics? This is when the result mathematical action does not depend on the value of the number, the unit of measurement used, and on who performs this action.
Ouch! Isn't this the women's restroom?
- Young woman! This is a laboratory for studying the indefinite holiness of souls upon ascension to heaven! Nimbus on top and arrow up. What other toilet?
Female... A halo on top and an arrow down is male.
If you have such a work of design art flashing before your eyes several times a day,
Then it is not surprising that you suddenly find a strange icon in your car:
Personally, I make an effort on myself to see minus four degrees in a pooping person (one picture) (composition of several pictures: minus sign, number four, degrees designation). And I do not consider this girl a fool who does not know physics. She just has an arc stereotype of perception of graphic images. And mathematicians teach us this all the time. Here is an example.
1A is not "minus four degrees" or "one a". This is "pooping man" or the number "twenty-six" in the hexadecimal number system. Those people who constantly work in this number system automatically perceive the number and letter as one graphic symbol.
The number "e" is one of the most important mathematical constants that everyone has heard about on school lessons mathematics. Concepture publishes a popular essay written by a humanist for the humanities, in which in plain language explain why and why the Euler number exists.
What do our money and the Euler number have in common?
While the number π (pi) is quite definite geometric meaning and it was used by ancient mathematicians, then the number e(Euler number) has taken its well-deserved place in science relatively recently and its roots go straight ... to financial issues.
Very little time has passed since the invention of money, when people guessed that the currency can be borrowed or lent under certain percentage. Naturally, the "ancient" businessmen did not use the concept of "percentage" familiar to us, but an increase in the amount by some certain indicator for a set period of time was familiar to them.
In the photo: a banknote worth 10 francs with the image of Leonhard Euler (1707-1783).
We won't go into the 20% APR example because it takes too long to get to the Euler number. Let's use the most common and illustrative explanation of the meaning of this constant, and for this we will have to dream a little and imagine that some bank offers us to deposit money at 100% per annum.
Thought-financial experiment
For this thought experiment you can take any amount and the result will always be identical, but starting from 1, we can come directly to the first approximate value of the number e. Because, let's say that we invest $1 in a bank, at a rate of 100% per annum at the end of the year we will have $2.
But this is only if interest is capitalized (added) once a year. What if they are capitalized twice a year? That is, 50% will be charged every six months, and the second 50% will be charged not from the initial amount, but from the amount increased by the first 50%. Will it be more beneficial for us?
Visual infographic showing the geometric meaning of the number π .
Of course it will. With capitalization twice a year, six months later we will have $ 1.50 in the account. By the end of the year, another 50% of $1.50 will be added, i.e. total amount will be $2.25. What will happen if capitalization is carried out every month?
We will be charged 100/12% (that is, approximately 8.(3)%) every month, which will be even more profitable - by the end of the year we will have 2.61 dollars. General formula to calculate the total amount for an arbitrary number of capitalizations (n) per year looks like this:
Total sum = 1(1+1/n) n
It turns out that with a value of n = 365 (that is, if our interest is capitalized every day), we get the following formula: 1(1+1/365) 365 = $2.71. From textbooks and reference books, we know that e is approximately equal to 2.71828, that is, considering the daily capitalization of our fabulous contribution, we have already come to an approximate value of e, which is already enough for many calculations.
The growth of n can be continued indefinitely, and the larger its value, the more accurately we can calculate the Euler number, up to the decimal point we need, for whatever reason.
This rule, of course, is not limited only to our financial interests. Mathematical constants are far from " narrow specialists» - they work equally well regardless of the application. Therefore, a good digging, you can find them in almost any area of life.
It turns out that the number e is something like a measure of all changes and "the natural language of mathematical analysis." After all, "matan" is tightly tied to the concepts of differentiation and integration, and both of these operations deal with infinitesimal changes, which the number characterizes so beautifully. e .
Unique Properties of the Euler Number
Having considered the most intelligible example of explaining the construction of one of the formulas for calculating the number e, briefly consider a couple more questions that directly relate to it. And one of them: what is so unique about the Euler number?
In theory, absolutely any mathematical constant is unique and each has its own history, but, you see, the claim to the title of natural language of mathematical analysis is quite a weighty claim.
The first thousand values of ϕ(n) for the Euler function.
However, the number e there are reasons for that. When plotting the function y = e x, it turns out amazing fact: not only y is equal to e x , the gradient of the curve and the area under the curve are equal to the same indicator. That is, the area under the curve from certain value y to minus infinity.
No other number can boast of this. For us, humanists (well, or just NOT mathematicians), such a statement says little, but mathematicians themselves say that this is very important. Why is it important? We will try to deal with this issue another time.
The logarithm as a premise of the Euler number
Perhaps someone remembers from school that the Euler number is also the base of the natural logarithm. Well, this is consistent with its nature, as a measure of all changes. Still, what does Euler have to do with it? To be fair, e is also sometimes called the Napier number, but the story would be incomplete without Euler, just as without mention of logarithms.
The invention of logarithms in the 17th century by the Scottish mathematician John Napier was one of the major events history of mathematics. At the celebration in honor of the anniversary of this event, which took place in 1914, Lord Moulton (Lord Moulton) said of him:
"The invention of logarithms was for scientific world like thunder among clear sky. No previous work led to it, predicted or promised this discovery. It stands alone, it breaks through human thought suddenly, without borrowing anything from the work of other minds and without following the then already known directions of mathematical thought.
Pierre-Simon Laplace, famous French mathematician and an astronomer, even more dramatically expressed the importance of this discovery: “The invention of logarithms, by reducing clocks painstaking work doubled the life of an astronomer." What impressed Laplace so much? And the reason is very simple - logarithms have allowed scientists to significantly reduce the time usually spent on cumbersome calculations.
All in all, logarithms made calculations easier—dropping them down one level on the complexity scale. Simply put, instead of multiplying and dividing, you had to perform addition and subtraction operations. And it's much more efficient.
e- base of natural logarithm
Let's take for granted the fact that Napier was a pioneer in the field of logarithms - their inventor. By at least He was the first to publish his discoveries. In this case, the question arises: what is the merit of Euler?
Everything is simple - he can be called the ideological heir of Napier and the man who brought the work of the life of a Scottish scientist to a logarithmic (read logical) completion. Is this interesting at all possible?
Some very important graph built using a natural logarithm.
More specifically, Euler derived the base of the natural logarithm, now known as the number e or Euler number. In addition, he entered his name in the history of science as many times as Vasya never dreamed of, who, it seems, managed to “visit” everywhere.
Unfortunately, specifically the principles of working with logarithms are the topic of a separate large article. So for now, it will suffice to say that thanks to the work of a number of dedicated scientists who literally devoted years of their lives to compiling logarithmic tables in a time when no one had even heard of calculators, the progress of science has greatly accelerated.
In the photo: John Napier - Scottish mathematician, inventor of the logarithm (1550-1617.)
It's funny, but this progress, in the end, led to the obsolescence of these tables, and the reason for this was precisely the appearance of hand calculators, which completely took over the task of performing this kind of calculation.
You may have heard about slide rules? Once upon a time, engineers or mathematicians could not do without them, but now it is almost like an astrolabe - an interesting tool, but more in terms of the history of science than everyday practice.
Why is it important to be the base of a logarithm?
It turns out that the base of the logarithm can be any number (for example, 2 or 10), but, precisely thanks to unique properties Euler numbers base logarithm e called natural. It is, as it were, built into the structure of reality - there is no escape from it, and it is not necessary, because it greatly simplifies the life of scientists working in various fields.
Here is an intelligible explanation of the nature of the logarithm from the site of Pavel Berdov. base logarithm a from the argument x is the power to which the number a must be raised to obtain the number x. Graphically, this is indicated as follows:
log a x = b, where a is the base, x is the argument, b is what the logarithm is equal to.
For example, 2 3 = 8 ⇒ log 2 8 = 3 (the base 2 logarithm of 8 is 3 because 2 3 = 8).
Above we saw the number 2 as the base of the logarithm, but mathematicians say that the most talented actor for this role is Euler's number. Let's take their word for it... And then we'll check to see for ourselves.
findings
Probably bad that within higher education so strongly separated natural and humanitarian sciences. Sometimes this leads to too strong a “skew” and it turns out that it is absolutely uninteresting to talk to a person who is well versed, for example, in physics and mathematics, on other topics.
And vice versa, you can be a first-class specialist in literature, but, at the same time, be completely helpless when it comes to the same physics and mathematics. But all sciences are interesting in their own way.
We hope that we, trying to overcome our own limitations within the framework of the impromptu program “I am a humanist, but I am undergoing medical treatment”, have helped you to learn and, most importantly, understand something new from an unfamiliar scientific field.
Well, for those who want to learn more about the Euler number, we can recommend several sources that even a person far from mathematics can understand if they wish: Eli Maor in his book “e: the story of a number” (“e: the story of a number ”) describes in detail and in an accessible way the background and history of the Euler number.
Also, in the "Recommended" section under this article, you can find the names of youtube channels and videos that were shot by professional mathematicians trying to clearly explain the Euler number so that even non-specialists can understand it Russian subtitles are available.
