# What is your favorite number?

1. Nov 15, 2016

### Greg Bernhardt

What is your favorite number and why? Is it lucky? Mathematically or aesthetically beautiful? Symbolic?

2. Nov 15, 2016

### jackwhirl

Zero. It's just so dang useful.

3. Nov 15, 2016

### Krylov

I would say $e$. Sorry, this choice is not very original, but its profound connection with differential equations and time evolution in general does it for me.

4. Nov 15, 2016

### QuantumQuest

Number 8. I think that is aesthetically beautiful, can be turned upside - down and still recognize it and turn it 90 degrees to the left or right and lo and behold: infinity!

5. Nov 15, 2016

### Staff: Mentor

42, of course!

6. Nov 15, 2016

### Staff: Mentor

$2$. 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.

Last edited: Nov 15, 2016
7. Nov 15, 2016

### Staff: Mentor

δ = 4.669201 .... Feigenbaum's constant. Got me interested in fractals in the late 1980's. Wrote lots of code, wasted lots of paper and printer toner. Had a ton of fun. Side effect: Had to learn postscript language run an Apple graphics printer. Which I still use sometimes. Piddling around can sometimes create the need to learn new things.

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

8. Nov 15, 2016

### QuantumQuest

Yes, but it is a diagram with the form of a slender figure-eight.

9. Nov 15, 2016

### SW VandeCarr

711! It must be really lucky.

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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:

• 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.
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

Last edited by a moderator: Nov 15, 2016
10. Nov 15, 2016

### kith

Although probably not what the OP had in mind, I really like the imaginary unit $i$ 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 $x + 1 = 0$ 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 $x$ is a negative number. The easiest equation of this type is $x^2 + 1 = 0$ and its solution is called the imaginary unit $i$. So $i$ 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, $i$ allows us to treat the elements of the vector space $\mathbb{R}^2$ 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: Nov 15, 2016
11. Nov 15, 2016

### Staff: Mentor

12. Nov 16, 2016

### Staff: Mentor

13. Nov 16, 2016

### PeroK

The number 39 has recurred in my life. When I was growing up, my mum's house was number 39 and my grandmother's house was also 39 When I started work, my first place in Nottingham was number 39, and now in London I have the luxury of a shed out back for my bike, which is number 39.

14. Nov 16, 2016

### HRubss

25, I love middle numbers (or numbers that end in 5) and it just so happened to be my jersey number when I was playing HS football.

15. Nov 16, 2016

### Staff: Mentor

Here's another favorite number of mine:
$$\omega = \inf_{ n \rightarrow \infty } \{ k \in \mathbb{R} \,\vert \, \text{ multiplications in }\mathbb{M}_n(\mathbb{R})\text{ can be done with } O(n^k) \text{ scalar multiplications } \}$$

16. Nov 16, 2016

### Staff: Mentor

Not sure about bringing good luck, but there's definitely convenience!

17. Nov 16, 2016

### Ryan_m_b

Staff Emeritus
I've always liked 64. It's just aesthetically nice to me, not to big or small and can be repeatedly halved to make integers all the way back to 1. There's nothing rational about that I admit lol. 72 feels nice too, again not a very large or small number but can be easily divided by 2, 3, 4, 6, 8, 9, 12, 18, 24 and 36.

18. Nov 16, 2016

### SW VandeCarr

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.

Last edited: Nov 16, 2016
19. Nov 16, 2016

### mister mishka

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

20. Nov 16, 2016

### Fervent Freyja

1. Simply because using it as the unit to count and measure has saved me time on a practical daily level. Without it, many simple things would take much longer and some things wouldn't be possible to do at all without a system to handle multiple things. What do other numbers mean without it? It is the backbone of modern civilization, really. A glorious number!

21. Nov 17, 2016

### Algr

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. Nov 17, 2016

### Bystander

Mort Walker fans? "Me?" 555, "The Triple Nickel."

23. Nov 17, 2016

### kith

No polynomial equations, yes. The precise statement is given by the fundamental theorem of algebra.

That's not an equation but a set of inequalities.

24. Nov 17, 2016

### Staff: Mentor

Two.

25. Nov 17, 2016

### Algr

But it is the clearest way to describe the issue, and I'm sure you can see the intent.