- #1

- 18,256

- 7,929

- Thread starter Greg Bernhardt
- Start date

- #1

- 18,256

- 7,929

- #2

- 211

- 147

Zero. It's just so dang useful.

- #3

S.G. Janssens

Science Advisor

Education Advisor

- 919

- 693

- #4

- 926

- 485

- #5

- #6

fresh_42

Mentor

- 13,582

- 10,710

##2##. I've always been fascinated by ##2+2=2\cdot2=2^2##. In addition it is the first "real" number, Peano's start off if you like, the first example of a characteristic ##\neq 0 ##, the reason why we can discuss this here, and last but not least: I like my Fermions.

Edit: And of course 4-O-9.

Edit: And of course 4-O-9.

Last edited:

- #7

jim mcnamara

Mentor

- 4,066

- 2,529

@QuantumQuest Isn't the analemma a kind of "sideways" eight as well?

- #8

- 926

- 485

Yes, but it is a@QuantumQuest Isn't the analemma a kind of "sideways" eight as well?

- #9

- 2,123

- 79

711! It must be really lucky.

52599924650976959931863318488933811704978493222438840788384049867456800858519627109962971815895829407761989523273989613166240592160728066791830921110583325384223941915518699768856067442228430711875183506196684127629207760992514388996081248311560565501487560204845163821641923809220050312208101063127499969844138656880052309752122743026732903118757119396312086020392059509885804305114006793280993357194895602004590284996860973925059973555659872762019899315757368299687262969384082363999063493658248887532005885961614610540578276150978503247731624736791292538671966856268880840621686066393351662438844927716665319288991511502025702085431424792467061438989980275576773108842401686277104782859771173580322319960096055106022395217615555952219577413327187387733231435848140376257112919659860272817733917738610299819592748198804257481101348268063360177474446673998635997041106331135126517436559802723582121416337043456626325345862219809021297932516701863097872987108497351835820547200333016972068550656124830289989676770916186728997149233116603220785416029541463917472609454981547946979891242801914671480585237159720392691003192503394464785990658223543865665459460525545587023519368579486154107458289733407560947991141902375683733195304136829543710856065441236162307589864514310521685384865525610643958597703960867767292409811104826438401553848868816730319778813006908085812008989374993313680134358920003349359672308698655778987953264796106854863809617212714853926001095596586480158755282227712998822643075582620840156082714809525403991813535210615603200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

**Calculator Use**

Instead of calculating a factorial one digit at a time, use this calculator to calculate the factorial n! of a number n. Enter an integer, up to 4 digits long. You will get the long integer answer and also the scientific notation for large factorials. You may want to copy the long integer answer result and paste it into another document to view it.

**What is a Factorial?**

A factorial is a function that multiplies a number by every number below it. For example 5!= 5*4*3*2*1=120. The function is used, among other things, to find the number of way “n” objects can be arranged.

Factorial

There are n! ways of arranging n distinct objects into an ordered sequence.

n

the set or population

In mathematics, there are n! ways to arrange n objects in sequence. "The factorial n! gives the number of ways in which n objects can be permuted."[1] For example:

**Factorial Problem 1**

**How many different ways can the letters in the word “document” be arranged?**

For this problem we simply take the number of letters in the word and find the factorial of that number. This works because

52599924650976959931863318488933811704978493222438840788384049867456800858519627109962971815895829407761989523273989613166240592160728066791830921110583325384223941915518699768856067442228430711875183506196684127629207760992514388996081248311560565501487560204845163821641923809220050312208101063127499969844138656880052309752122743026732903118757119396312086020392059509885804305114006793280993357194895602004590284996860973925059973555659872762019899315757368299687262969384082363999063493658248887532005885961614610540578276150978503247731624736791292538671966856268880840621686066393351662438844927716665319288991511502025702085431424792467061438989980275576773108842401686277104782859771173580322319960096055106022395217615555952219577413327187387733231435848140376257112919659860272817733917738610299819592748198804257481101348268063360177474446673998635997041106331135126517436559802723582121416337043456626325345862219809021297932516701863097872987108497351835820547200333016972068550656124830289989676770916186728997149233116603220785416029541463917472609454981547946979891242801914671480585237159720392691003192503394464785990658223543865665459460525545587023519368579486154107458289733407560947991141902375683733195304136829543710856065441236162307589864514310521685384865525610643958597703960867767292409811104826438401553848868816730319778813006908085812008989374993313680134358920003349359672308698655778987953264796106854863809617212714853926001095596586480158755282227712998822643075582620840156082714809525403991813535210615603200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Instead of calculating a factorial one digit at a time, use this calculator to calculate the factorial n! of a number n. Enter an integer, up to 4 digits long. You will get the long integer answer and also the scientific notation for large factorials. You may want to copy the long integer answer result and paste it into another document to view it.

A factorial is a function that multiplies a number by every number below it. For example 5!= 5*4*3*2*1=120. The function is used, among other things, to find the number of way “n” objects can be arranged.

Factorial

There are n! ways of arranging n distinct objects into an ordered sequence.

n

the set or population

In mathematics, there are n! ways to arrange n objects in sequence. "The factorial n! gives the number of ways in which n objects can be permuted."[1] For example:

- 2 factorial is 2! = 2 x 1 = 2

-- There are 2 different ways to arrange the numbers 1 through 2. {1,2,} and {2,1}. - 4 factorial is 4! = 4 x 3 x 2 x 1 = 24

-- There are 24 different ways to arrange the numbers 1 through 4. {1,2,3,4}, {2,1,3,4}, {2,3,1,4}, {2,3,4,1}, {1,3,2,4}, etc. - 5 factorial is 5! = 5 x 4 x 3 x 2 x 1 = 120
- 0 factorial is a definition: 0! = 1. There is exactly 1 way to arrange 0 objects.

For this problem we simply take the number of letters in the word and find the factorial of that number. This works because

Last edited by a moderator:

- #10

kith

Science Advisor

- 1,358

- 453

Although probably not what the OP had in mind, I really like the imaginary unit [itex]i[/itex] for its mathematical beauty.

Starting with the natural numbers, people have struggled with the expansion of the number system for centuries. Successive expansions can be put in a very elegant scheme, namely the introduction of new solutions to polynomial equations which didn't have solutions previously. For example the equation [itex]x + 1 = 0[/itex] doesn't have a solution using only natural numbers, but it has a solution if we introduce negative numbers.

Naturally, we may be interested in the question whether the process of inventing new numbers (negative numbers, fractions, irrationals, ...) comes to an end and it turns out it does. If we already have the real numbers, we mainly need to invent solutions for one additional type of polynomial equation: those where the square of [itex]x[/itex] is a negative number. The easiest equation of this type is [itex]x^2 + 1 = 0 [/itex] and its solution is called the imaginary unit [itex]i[/itex]. So [itex]i[/itex] kind of marks the end point of a long mathematical journey. (In technical terms, the complex numbers are said to be "algebraically closed".)

Viewed from a different angle, [itex]i[/itex] allows us to treat the elements of the vector space [itex]\mathbb{R}^2[/itex] as numbers (more precisely we get the field of the complex numbers). This is really cool and remarkable and the additional structure leads to many powerful and beautiful theorems in complex analysis.

Starting with the natural numbers, people have struggled with the expansion of the number system for centuries. Successive expansions can be put in a very elegant scheme, namely the introduction of new solutions to polynomial equations which didn't have solutions previously. For example the equation [itex]x + 1 = 0[/itex] doesn't have a solution using only natural numbers, but it has a solution if we introduce negative numbers.

Naturally, we may be interested in the question whether the process of inventing new numbers (negative numbers, fractions, irrationals, ...) comes to an end and it turns out it does. If we already have the real numbers, we mainly need to invent solutions for one additional type of polynomial equation: those where the square of [itex]x[/itex] is a negative number. The easiest equation of this type is [itex]x^2 + 1 = 0 [/itex] and its solution is called the imaginary unit [itex]i[/itex]. So [itex]i[/itex] kind of marks the end point of a long mathematical journey. (In technical terms, the complex numbers are said to be "algebraically closed".)

Viewed from a different angle, [itex]i[/itex] allows us to treat the elements of the vector space [itex]\mathbb{R}^2[/itex] as numbers (more precisely we get the field of the complex numbers). This is really cool and remarkable and the additional structure leads to many powerful and beautiful theorems in complex analysis.

Last edited:

- #11

Mark44

Mentor

- 34,178

- 5,793

OK, I'll bite. What's the significance of this number to you?Edit: And of course 4-O-9.

It makes me think of the Beach Boys song, "409 " -- http://www.bing.com/videos/search?q...t=she's+real+fine+my+409+beach+boys&FORM=VDRE

- #12

fresh_42

Mentor

- 13,582

- 10,710

You know I'm simple minded enough to like their music.OK, I'll bite. What's the significance of this number to you?

It makes me think of the Beach Boys song, "409 " -- http://www.bing.com/videos/search?q=she's+real+fine+my+409+beach+boys&qpvt=she's+real+fine+my+409+beach+boys&FORM=VDRE

- #13

- 14,773

- 7,006

- #14

- 66

- 1

- #15

fresh_42

Mentor

- 13,582

- 10,710

$$ \omega = \inf_{ n \rightarrow \infty } \{ k \in \mathbb{R} \,\vert \, \text{ multiplications in }\mathbb{M}_n(\mathbb{R})\text{ can be done with } O(n^k) \text{ scalar multiplications } \}$$

- #16

NascentOxygen

Staff Emeritus

Science Advisor

- 9,244

- 1,072

Not sure about bringing good luck, but there's definitely convenience!711! It must be really lucky.

- #17

Ryan_m_b

Staff Emeritus

Science Advisor

- 5,844

- 711

- #18

- 2,123

- 79

711 implies convenience like the store. 711! is my lucky number but it is convenient to calculate it online nowadays. Poor Isaac Newton would have had to do it by hand. However, I've read that he enjoyed doing long tedious calculations.Not sure about bringing good luck, but there's definitely convenience!

Last edited:

- #19

- 41

- 32

2, I honestly do not know why, but I've always liked that number ^^

- #20

Fervent Freyja

Gold Member

- 637

- 583

- #21

- 435

- 120

. So [itex]i[/itex] kind of marks the end point of a long mathematical journey. (In technical terms, the complex numbers are said to be "algebraically closed".)

Viewed from a different angle, [itex]i[/itex] allows us to treat the elements of the vector space [itex]\mathbb{R}^2[/itex] as numbers (more precisely we get the field of the complex numbers). This is really cool and remarkable and the additional structure leads to many powerful and beautiful theorems in complex analysis.

So there are no unsolvable equations in the complex numbers? I don't think so. In fact I've brought up one previously:

Y<1

Y+X<=1

Solve for X (That works for all reals.)

The last time I brought this up people were using dodges that sounded a lot more like politics then math. (Hence the reals stipulation above. )

As for my favorite number. Well, zero is my hero. :) And there appears to me more then one kind of zero in the reals.

- #22

Bystander

Science Advisor

Homework Helper

Gold Member

- 5,193

- 1,213

Zero. It's just so dang useful.

Mort Walker fans? "Me?" 555, "The Triple Nickel."Well, zero is my hero. :)

- #23

kith

Science Advisor

- 1,358

- 453

NoSo there are no unsolvable equations in the complex numbers?

That's not an equation but aY<1

Y+X<=1

- #24

Evo

Mentor

- 23,156

- 2,810

Two.

- #25

- 435

- 120

But it is the clearest way to describe the issue, and I'm sure you can see the intent.That's not an equation but asetofinequalities

- Last Post

- Replies
- 81

- Views
- 7K

- Last Post

- Replies
- 25

- Views
- 2K

- Last Post

- Replies
- 24

- Views
- 3K

- Last Post

- Replies
- 32

- Views
- 4K

- Last Post

- Replies
- 53

- Views
- 6K

- Last Post

- Replies
- 13

- Views
- 383

- Last Post

- Replies
- 24

- Views
- 4K

- Last Post

- Replies
- 9

- Views
- 2K

- Last Post

- Replies
- 76

- Views
- 10K

- Replies
- 4

- Views
- 649