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0:28

Ноль в нулевой степени. Неопределенность.

3:11

Факториал и 0!

5:02

Число сочетаний по нулю

5:30

почему 13 несчастливое число?

6:04

несчастливое число в Японии

6:32

Есть только МИГ, между прошлым и...

7:17

Почему нет Нобелевской премии по математике

8:39

Какое самое большое число?

9:41

Вы не поверите, но это 5!

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qwerty

новости

новости науки

наука

исследования

научпоп

математика

логика

задачки

задачи по математике

математика егэ

решение задач

топ

математические истории

делить на ноль

ноль в степени ноль

факториал

число сочетаний

теория вероятности

доктор стрэндж

алгебра

ошибки в математике

решебник

гдз

почему нельзя делить на 0

топ 10

магия

мракобесие

helloween

день святых

хеллоуин

кошмар перед рождеством

реальнаяматематика

ноль

00:00:01

some quite interesting facts and

00:00:04

answer some funny questions

00:00:06

that arise in mathematics around it

00:00:11

[music]

00:00:13

hello everyone, glad to see you on the

00:00:16

qwerty channel in our mathematics section,

00:00:18

I hope that you have been subscribed to this channel for a long time

00:00:20

so as not to miss new

00:00:21

releases in particular

00:00:23

and mathematically, but who hasn’t done this yet,

00:00:25

do it now and let’s start with this

00:00:27

question, many have already wondered

00:00:30

why you can’t divide by zero,

00:00:32

there are a lot of videos about this and I

00:00:34

won’t talk about it now, but the more interesting question is about

00:00:36

0 to the zeroth power and I read more than once and

00:00:39

more than twice about the fact that in mathematics you

00:00:41

can decide for yourself: some write that any

00:00:43

number to the zero power is equal to one,

00:00:45

others write 0 to any power is 0 and

00:00:48

what is something 0 to 0 units and or 00 to

00:00:52

0 is uncertainty is formally expressed by the

00:00:55

expression 0 0 is not defined, it is often defined

00:00:58

before it is defined, that is, they simply say that

00:01:01

0 in zero is set equal to one of which

00:01:05

and on units they are

00:01:06

zero considerations can be several one

00:01:10

of them that if for example you take a

00:01:12

function x of degree x and calculate the limit of

00:01:15

this function at x tending to 0,

00:01:17

that is, people are 1 2 powers of 2 1 3 by

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3 one millionth to the power of one

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millionth and so on you will

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approach zero,

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the closer you are to zero the closer

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this value will come to one the

00:01:29

limit will really be wound or,

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nevertheless, it is a big mistake to assume that

00:01:34

any infinitesimal function to the

00:01:37

infinitesimal power must be equal to

00:01:39

one and here is a counterexample, take

00:01:41

this expression and to the power of minus 1 xor

00:01:45

we raise the power of x

00:01:47

if x tends to zero then we just

00:01:50

get that the degree is ours the big one

00:01:52

is outside the brackets,

00:01:53

it tends to 0 - just tx and in the

00:01:56

brackets we have a certain constant a

00:01:58

which is raised to the power of minus 1, well,

00:02:01

like 0, that is, the power of minus

00:02:04

infinity and any number a is greater than

00:02:06

one which we raise to the power of

00:02:08

minus infinity it will tend

00:02:10

to zero, yes, for example, as a quality I can take

00:02:13

a two there are threes, this means it seems that it

00:02:15

turns out that then the limit of this

00:02:16

expression should be one, but this is not

00:02:18

so because if you just honestly

00:02:20

raise the degree to a power, yes you

00:02:22

will get a to minus 1, so for even

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2 teach corresponds one second for an

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even 3 2 3 and so on all this limit

00:02:29

can be anything

00:02:30

hence the moral when you do

00:02:33

higher mathematics you get an

00:02:35

uncertainty of the form 0/0

00:02:38

you can’t replace one with something, but if you have

00:02:41

strictly expressions like 0 in zero

00:02:43

some scientists have agreed to consider

00:02:46

this as a unit, just like that it’s more convenient for

00:02:49

some reasons, and I’ll

00:02:51

repeat once again this is the so-called irremovable

00:02:53

discontinuity for a function of two variables if

00:02:55

you take functions of degree sometime from the

00:02:58

point 0 0 unfortunately the

00:03:00

irremovable discontinuity is a continuous function, but it wo

00:03:02

n’t be like you will not determine

00:03:03

the value at this point, here’s a story

00:03:06

by the way, it’s interesting that there is a neighboring

00:03:10

problem about 0 factorial,

00:03:11

you all know that the factorial of a number is the

00:03:14

product of all numbers from 1 to this

00:03:17

number, we are now talking about natural

00:03:18

numbers, that is, 5 factorial is one

00:03:21

two by three by four by five one hundred and

00:03:22

twenty, what is 0 factorial then?

00:03:26

Well, in theory it’s not clear at all what

00:03:28

because we defined it for naturals and in

00:03:31

fact you would be right in saying that

00:03:33

it’s not clear that usually they just

00:03:35

define 0 factorial as a unit

00:03:38

why again, exactly as a unit and that’s

00:03:41

why, well, let’s see that n

00:03:43

factorial is any number factorial is n

00:03:47

minus 1 factorial needed by n

00:03:49

logical but really if a minus 1

00:03:52

factorial as the product of all numbers

00:03:53

from 1 to n minus 1 multiplied by r we get

00:03:56

n factorial that means if you substitute this equality,

00:03:58

it is equal to one, we get

00:04:01

that 0 factorial multiplied by 1 is equal to

00:04:04

one factor and one factor one

00:04:06

divide 1 factorial by 1, we get 0

00:04:09

factorial is also one, this is a so-so

00:04:11

proof because this is

00:04:13

the equality that n minus 1 factorial

00:04:14

multiplied by n equals n factorial, in

00:04:17

theory it should only work for those

00:04:19

natural m for which n n minus 1

00:04:22

natural and because only for them

00:04:24

we have defined the concept of factorial,

00:04:26

but here I’m just illustrating how convenient it is to

00:04:29

reason to get the value

00:04:31

-1 factorial plus 0 factorial can be said in another way

00:04:36

n factorial is a quantity before

00:04:38

nova of n elements, yes, if we have

00:04:40

n different objects, then the number of ways

00:04:43

their representative is factorial is a question of

00:04:45

how many ways do you have to rearrange

00:04:47

0 objects,

00:04:49

you can say that I have one way

00:04:52

there is nothing on the children's table, this is

00:04:54

the only way to rearrange any

00:04:56

set of objects or an empty one, well, therefore,

00:04:59

units and the third question is related to zero,

00:05:03

which can be analyzed about the number of

00:05:05

combinations csm by zero, but here everything is

00:05:08

much simpler for those who are familiar with this

00:05:10

concept to the number of combinations, that is,

00:05:13

ways select

00:05:14

0 objects from and pieces without taking into account the order

00:05:19

where the order is accordingly not important to us,

00:05:21

here is one method, another, we have not chosen

00:05:24

anything, here is the only way,

00:05:25

therefore, the csn panels are also units, well

00:05:29

let's move on. The second is a rather funny

00:05:32

question that can be considered about

00:05:34

lucky and unlucky numbers, in

00:05:36

particular many they know that 13 is an

00:05:38

unlucky number, but do you know why, that is, it’s very

00:05:42

funny that the history of this issue goes back

00:05:44

to biblical times, as you remember there was the

00:05:46

Last Supper, 12 people were 13 m

00:05:48

came here since then until the present day

00:05:52

before wanted something 13 something bad before

00:05:53

it has come to light that, as you know, hotels don’t have

00:05:56

13 of their rooms; in many planes they don’t

00:05:58

have 13 rows and so on, simply because

00:06:01

such a story was

00:06:02

told, few people know this, but

00:06:04

it’s interesting that in different countries

00:06:05

different numbers are considered unlucky, in

00:06:08

particular for example in Japan and in

00:06:10

some other eastern countries the most

00:06:12

unlucky number is 4 because

00:06:14

the corresponding rubles are read the same way

00:06:17

as death, and many people think this is very

00:06:20

bad, so we do

00:06:22

n’t seem to have the same prejudices; it’s

00:06:23

funny that in some

00:06:25

strange countries 7 is an unlucky number, well and here

00:06:29

we seem to consider the lucky

00:06:30

seven the

00:06:31

third moment that I want

00:06:32

to talk about I literally just recently

00:06:34

came across and decided to share with you

00:06:36

about the mega, you know, yes there is only

00:06:40

a moment between the past and the future,

00:06:45

what is a moment, well, someone thinks that a moment

00:06:49

is like a moment before that there is such a very

00:06:51

very small period of time

00:06:52

that is not defined in any way, it’s just a

00:06:55

philosophical value, a small

00:06:57

interval of three, in fact, no VIC,

00:07:00

this is quite a unit of

00:07:02

time measurement, yes, just like a second, just like a

00:07:05

minute in size, a moment is equal to

00:07:07

approximately one hundredth of a second,

00:07:09

so for the future do you know how much there will be

00:07:11

between the past and the future and what

00:07:13

life is 4 moments that I want

00:07:16

to talk about

00:07:17

recently a chair in a dialogue with one of my

00:07:19

colleagues when we were discussing the Nobel

00:07:22

Prize and somehow it came up about the

00:07:24

lack of a Nobel Prize in

00:07:25

mathematics and I was surprised to discover that

00:07:27

my colleague shares the misconception of many

00:07:30

people is that the Adobe Russian Prize in

00:07:32

Mathematics is not awarded because it means that

00:07:35

Nobel stole his wife from some kind of mathematics,

00:07:37

you in fact, in the opinion of

00:07:39

at least the majority of historians, this is not true for

00:07:41

one simple reason, Nobel did not

00:07:43

have a wife, it was really mathematics

00:07:45

which but Billy there was a conflict, but this is

00:07:47

only one version of why the Nobel

00:07:50

Prize is not awarded, there are two that are

00:07:52

somewhat more likely, and so

00:07:54

the number and we won’t get into the head of why there

00:07:56

she left only five

00:07:58

disciplines, not including mathematics, the question is,

00:08:00

but more likely what the versions converge on

00:08:03

is the first one that at that time there was already a

00:08:07

separate prize in mathematics, which

00:08:09

was established by the king of Sweden, and therefore,

00:08:12

in order not to repeat himself, he decided to

00:08:13

give his prize to me as a mathematician, but an even

00:08:16

more popular version is that

00:08:18

Nobel believed that the prize should be given

00:08:20

only for those discoveries that have a

00:08:22

clear practical meaning I wonder what the meaning is, well,

00:08:25

for example, these are done in physics, in

00:08:27

chemistry, and so on, and in mathematics, they

00:08:29

say, well, it’s still not immediately

00:08:31

obvious practical application, so the

00:08:33

Nobel Prize is not awarded, I

00:08:36

honestly believe in this version more,

00:08:38

but here’s another funny question that

00:08:41

came up I was no longer with a

00:08:43

mathematician colleague, but with one child;

00:08:45

this man was only 7 years old, but

00:08:47

with his answer he puzzled me

00:08:49

because somehow, having gotten into a conversation with a

00:08:51

complete stranger,

00:08:52

not a boy, I decided to joke with him and

00:08:54

asked what the largest number he

00:08:57

knows and well I expected to laugh a

00:09:00

little because he would probably say a

00:09:02

million or a billion or maybe

00:09:03

google or something else, but I can always

00:09:06

say what about a billion plus 1 and so

00:09:08

on, but he gave a comprehensive, absolutely

00:09:10

accurate answer and I couldn’t figure out how to

00:09:13

strongly refute his statements

00:09:15

found the largest number, you can

00:09:17

pause the video and think and

00:09:19

then find out the answer and the correct answer of

00:09:23

this boy was very elegant 31

00:09:26

according to that you can’t come up with a larger number

00:09:30

32 there 33 in months we don’t have so the

00:09:33

thirty-first number is the

00:09:35

largest so he is right, and finally,

00:09:38

our hit parade is

00:09:40

closed by one rather funny story

00:09:43

that recently began

00:09:45

to visit again for the first time, I probably saw it 5 years

00:09:47

ago, they were

00:09:49

gossiping about it for a long time, generally correctly

00:09:52

and it was wrong, they said there they almost

00:09:54

cursed, they said that Yes, you don’t

00:09:56

know the procedure there, in

00:09:58

fact, I’ve already slightly spoiled why

00:10:01

this is really all true

00:10:03

because on the right we count 5 days, again

00:10:07

factorial up to 5 factorial is exactly

00:10:09

120 and indeed the left side is equal to

00:10:11

120

00:10:12

well, based on this problem I I came up with a

00:10:15

slightly different problem that

00:10:16

may also seem interesting to you, because

00:10:18

at least it seems to me that

00:10:21

this equality is surprising, but

00:10:24

you can truly prove why with your version,

00:10:28

write in the comments and I’ll

00:10:30

say goodbye with this, don’t forget to like if

00:10:31

you liked it and see you again on

00:10:33

channel qwerty bye bye

00:10:39

[music]

Description:

НЕ расскажем почему на ноль делить нельзя (ну слишком банально). В математике полно других занятных фактов и неопределенностей, которые вызывают жаркие споры в математических кругах. Готов ли твой мозг принять такую реальность? Добро пожаловать на урок математической магии к Георгию Вольфсону! 0:28 Ноль в нулевой степени. Неопределенность. 3:11 Факториал и 0! 5:02 Число сочетаний по нулю 5:30 почему 13 несчастливое число? 6:04 несчастливое число в Японии 6:32 Есть только МИГ, между прошлым и... 7:17 Почему нет Нобелевской премии по математике 8:39 Какое самое большое число? 9:41 Вы не поверите, но это 5! Подписаться на лучший научпоп на ΥοuTube: https://www.youtube.com/user/qwrtru?sub_confirmation=1 Читать наши улётные новости ВКонтакте: http://vk.com/qwrtru Прокачивать мозг в нашем Instagram: https://www.facebook.com/unsupportedbrowser Следить за нами в Facebook: https://www.facebook.com/unsupportedbrowser Наш telegram @QWERTY_LIVE: https://tele.click/joinchat/AAAAAEXgtlwGpajYh_7_5Q Поддержать наш проект можно по ссылке: https://youtube.streamlabs.com/qwrtru Контакт для связи: [email protected] При поддержке студии интернет-маркетинга Mevix. Музыка: Phillip Gross; Rusty Sharks

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