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Showing posts with label factorial. Show all posts
Showing posts with label factorial. Show all posts

## 2.08.2011

### The table of factorials to 255

Exact values of a factorial of natural numbers to 50 we have already considered. In practice, at mathematical calculations, use approximate values of a factorial which are collected in the table of factorials to 255 is more often.

### Factorial

Factorial in the mathematician name product of all natural numbers, including the specified number. The factorial by an exclamation mark after number, for example 4 is designated!. So, if you have met an exclamation mark in the mathematician, it at all does not mean "Vau! Number!". It simply factorial. From sacred mathematical texts it is necessary to learn one phrase "a zero Factorial it is equal to unit". Why the zero factorial is equal to unit? Read under the reference. Exact values of factorials of numbers to 50 are resulted in drawing.

 Factorial
On a picture it is shown how to consider a factorial for natural number 7. Calculation of a factorial of other numbers is made in the same way: all numbers from one to specified before an exclamation mark are multiplied among themselves.

The factorial of 1 (unit) is equal to unit.
1! = 1
The factorial of 2 (two) is equal to two.
2! = 1 · 2 = 2
The factorial of 3 (three) is equal six.
3! = 1 · 2 · 3 = 6
The factorial of 4 (four) equals to twenty four.
4! = 1 · 2 · 3 · 4 = 24
The factorial 5 is equal hundred twenty.
5! = 1 · 2 · 3 · 4 · 5 = 120
Well and so on.

In a general view the formula for a factorial finding can be written down so:

n! = 1 · 2 · 3 · 4 · ... · (n - 2) · (n - 1) · n

The table of factorials to 255 is presented on separate page.

By the way, if you go at the wheel the car and will see an exclamation mark in a triangle on a white or yellow background is not a lesson of mathematics with factorials, it is a traffic sign "Attention!".

 Factorial )))
Here it is not necessary anything the friend on the friend to multiply. It is necessary to postpone away the beautician, to cease to stir by a mobile phone and more strong to keep for a car wheel. Attentively look not on the parties, and at road. Ahead there can be unpleasant surprises. That unpleasant surprises on road did not turn to unpleasant situations, them designate this traffic sign.

## 2.05.2011

### Enter number, how many there will be a factorial of three

"Enter number, how many there will be a factorial of three" Ogo! Here it is an ambush for blondes! Judging by that is written "enter number" is a site of any pervert from mathematics asks to enter into a window number. I would be frightened of such request! Same it is necessary to be such sadist that the visitors by means of a torture factorial to arrange! And it would be desirable to ask: "And you, the clever man, can count a factorial of four?! Or without the calculator poorly?!" Is not present, with this disgrace it is necessary to struggle. Anybody from Internet users is not obliged to know factorials - the Internet exists for all. It is obvious discrimination of blondes!

With a view of struggle against similar mathematical rudeness, we will create the small table of factorials for the aid to poor blondes and not only to it.

0! = 1
1! = 1
2! = 1 х 2 = 2
3! = 1 х 2 х 3 = 6
4! = 1 х 2 х 3 х 4 = 24
5! = 1 х 2 х 3 х 4 х 5 = 120

And so, the zero factorial is equal to unit, unit factorial is equal to unit, the factorial of two is equal to two, the factorial of three is equal six, the factorial of four is equal twenty four, the factorial of five is equal hundred twenty. I think, it will be quite enough for personal self-defence on the Internet.

By the way, as chance offers can ask those, who considers itself strongly literate, whether they know, how many figures at a factorial, well... For example, two hundred fifty five? In this number of five hundred five figures!!!

255! = 3350850684932979117652665123754814942022584063591740702576779884286208799035732771005626138126763314259280802118502282445926550135522251856727692533193070412811083330325659322041700029792166250734253390513754466045711240338462701034020262992581378423147276636643647155396305352541105541439434840109915068285430675068591638581980604162940383356586739198268782104924614076605793562865241982176207428620969776803149467431386807972438247689158656000000000000000000000000000000000000000000000000000000000000000

This number is five times longer, than the well-known number googol, in which only one unit and hundred zeroes. And at us five hundred five it is not simple zeroes, and different numbers)))

I hope, to anybody from you will not offer: "Enter number, how many there will be a factorial of two hundred fifty five")))

## 11.13.2010

### Why is the factorial of zero equal to unit?

A factorial appeared in mathematics near 1800. In mathematics a factorial is name work of all natural numbers, including indicated. Designate a factorial an exclamation mark, written after a number.

5! = 1 х 2 х 3 х 4 х 5 = 120

The official version of appearance of factorial in mathematics I do not want to search, because I know perfectly, how it was actually. And there was all so.

Completing all letups on a theory and practice of factorial calculations, Scientist bore the creation on the court of Saint Mathematical Inquisition. Functions of supervision after mathematicians on behalf of Saint Mathematical Inquisition in this locality executed Saint Scientific Infirmities. Responsibility on him lay enormous, work was very much, more precisely, to do it was in general nothing. Therefore Saint Scientific Infirmities selflessly dug up in a nose. After this employment he was found by Scientist.

Executed in due form bureaucratic art, a folder with the theory of factorials lay down on feet before the eyes of Saint Scientific Infirmities. Infirmities were taken out by a finger from a nose, fastidiously made a wry face and began the same finger to leaf a folder. He checked content of folder for accordance to "Law on registration of papers, presented to Saint Mathematical Inquisition". Obvious occasion to say no to Scientist in consideration of his papers was not. To enormous regret of Saint Scientific Infirmities. Vexation affected his official. An at this time leading hand reached the form of Official Statement, Book of Registration of Visitors, Book of Registration of Incoming Documents, Book of Registration of Get-away Visitors and other treasures of Responsible Leading already.

Carefully collating everything, that was written by Scientist, with the "Explanatory dictionary for muddle-headed Bureaucrats. Rules of writing of Words and Letters" (this masterpiece was hidden from the eyes of visitors under a vulture "For the official use"), said Saint Scientific Infirmities:

"Your materials will be considered in the term set by Law".

His leading finger again submerged in a nose, continuing the interrupted work. It meant the end of audience.

The time of consideration of document fixed by law passed. A scientist again came to Saint Scientific Infirmities. Discontentedly made a wry face infirmity, scratched the back of head, feeding speech goes to remember about what, then got a folder with a factorial and began attentively it to study. An answer he must give today because the time taken on bureaucratic procedure made off already. Twisted infirmities backward, checking, firmly how enough Leading Arm-chair sticks to under them. Leading Arm-chair squeaked treacherously.

"You, Scientist, must know that a zero is a natural number", - said Infirmities and with relief breathed, - "All your factorials will equal a zero. On determination."

I want to remind readers, that events took place on a wild west, where a zero all consider a natural number.

"Your work very interesting. It will be really it is sorry me, if she will remain known to nobody", - continued Infirmities - "I would assist to the publication of your work, if you will add me in coauthors."

It is a widespread in science reception. Through him hacks do to itself a career in science. Suggestion of Infirmity did not surprise Scientist. He answered:

"I will be happy to be the coauthor of such prominent scientist, as you. But how to be with a zero?"

"I see no problems," - Infirmities demonstrated a complacency and grandeur, - "It is said In Saint Mathematical Limning, that any number, increased on a zero, equals a zero. But in this Limning there is not a single word about the factorial of zero. I will write an address to Saint Mathematical Inquisition with a request making alteration in text of Saint Mathematical Limning. Let them write, that the factorial of zero is equal to unit."

An agreement was attained. A scientist here entered a coauthor in the work. Wrote saint Scientific Infirmities appeal. This advanced study was sent for consideration of higher scientific leaders.

Higher scientific leaders knew the rules of bureaucratic games well. The name of Scientist they did not touch. The name of the inferior every higher scientific leader wiped and inscribed the name into place of coauthor. As a result of it a hole appeared in the coauthors of Scientist.

From the same pores in Saint Mathematical Limning there is a masterpiece of scientific thought: Gospel says of from Rules of Increase, that a zero, increased on unit, will be equal to the zero

0 х 1 = 0

A Gospel asserts from Factorial, that a zero, increased on unit, is equal to unit

0 х 1 = 1

Whew mathematics grows into a marasmus.