Page 1 of 4

### A Universe of Numbers. [Join Any Time]

Posted: Thu Aug 27, 2020 10:40 pm
Jake had created a pocket universe. He was sad, and lonely, so he created a plethora of empty husks, all tasked with filling the little universe with numbers. Lots and lots of numbers. All of the numbers, if they could. All he needed were willing participants..
He called out to the multiverse, trying to attract visitors. Will this be the beginning of a Universe of Numbers, or the death of yet another failed creation? Only time will tell..

He laid out rules for this universe, all which must be followed, both literally, and spiritually. He didn't appreciate literary loopholes, only mathematical ones.

One: Thou shalt keep things simple: Only one mathematical operator at a time.
Two: No number can be created without having the full building blocks behind it, you must use the full numbers, but only the numbers consisting only of digits, before you. This also means you cannot rip and tear digits out to create a Frankenstein's Monster of a number.
Three: What game would be fun without multiple players? Your equation cannot contain all numbers you have made yourself, and you cannot post if you have made the most recent post. They must also be color coded by the person who first created it.
Four: No number can be created out of nothing, your post cannot add in new numbers.
Five: What would a universe be with only cold, calculating hands? You may comment anything in addition to your submission, provided that it is absolutely clear that the two are separated entities.

Whoever creates the most unique numbers before this inevitably fails wins.

Current colors and numbers:
Jake The Wolfie (Orange) (-4256, -3, -1, i, 1, (pi/3)i, Sqrt(2), pi, 4, tau, 17, 27, 128, 255.75+i)
StrangerCoug (Blue) (-0.25+i, -pi/2, -pi/8, -i, 0, 1/2 + i*sqrt(3)/2, pi/6, pi/3, 2, e, 10, 256)
Ircher (Purple) (-0.25, pi/2, 3, e^2 - e*sqrt(2), 5, 7, 4256)
NotAJumbleOfNumbers (#CCFFDD) (NaN, 15, 19)
Farren (Green) (-2)

And in the first post, Jake said "Let there be 1." And so the game had begun.

Posted: Fri Aug 28, 2020 8:18 am
1, of course, was the loneliest number, and that would never do for Jake the Wolfie. So he had summoned StrangerCoug from the multiverse to help him out.

StrangerCoug was a software engineer back home, as well as a bit of a hack writer as a hobby. He could never dream of writing anything as poetic as the greats of Shakespeare and the like, but that was not what Jake needed from Coug. He needed other numbers besides just 1, and there were strict rules on how to create other numbers.

"Well, let's see," StrangerCoug said. "I'd increment, like you can do with the ++ operator in many programming languages I know, but I don't know if you have an operator like that in your pocket universe. But luckily, you increment a number by adding 1 to it, and 1 is exactly what you have. So there you have it: 1 + 1 = 2. I'll be glad to stick around to help!" He gave a bit of an uncanny smile, almost like the Cheshire Cat.

Posted: Fri Aug 28, 2020 10:42 am
I see your 2, and I do the following:

1-2=-1

A negative element has been created. Such an interesting discovery, and so close to the origin.

Posted: Fri Aug 28, 2020 11:00 am
This negative element intrigued Coug. Of course he had to have fun with it. He took the -1 that Jake created and tried to combine it with the positive 1 that was so lonely before. From it, he created a pure nothingness, as -1 + 1 = 0, neither positive not negative, but certainly even.

Posted: Fri Aug 28, 2020 11:58 am
While it would be easier to add, Jake multiplied.

2x2=4

Certainly not a big number, but the biggest so far.

Posted: Fri Aug 28, 2020 1:31 pm
Coug was impressed, but at the same time he was jealous. So far, the numbers -1, 0, 1, 2, and 4 existed, and he wanted a number bigger than all of those combined. FAR bigger, in fact. He was hungry with powerâ€”and powers would be the next operation he would use. Exponentiation was simply repeated multiplication, and nowhere in the rules did he find that he was limited to addition, subtraction, multiplication, and division. Thus he created 4^4 = 256. This, he thought, could open up a lot of opportunities for number creation, and Coug saw that it was good.

Posted: Fri Aug 28, 2020 1:54 pm
Jake flipped Coug the finger as he square rooted 2. Who cares aboit large numbers, when irrational numbers were key?

Sqrt(2) = Sqrt(2)

Posted: Fri Aug 28, 2020 2:21 pm
Yet something was still missing as Ircher entered the scene. "How can you have irrationals before rationals!" Ircher exclaimed. And so it was on the very next instant, the rationals entered being as something truly fantastic.

-1 / 4 = -1/4

Posted: Fri Aug 28, 2020 2:48 pm
I'll square root until there's nothing left to root!

Sqrt(-1) = i

And within an instant, the 1 dimensional line became a 2 dimensional plane.

Posted: Fri Aug 28, 2020 4:48 pm
A newcomer had entered the Universe of Numbers and created its first rational non-integer. Soon after, the very creator of that universe created the imaginary unit. The imaginary plane, so far, could only be traversed along the real or imaginary axisâ€”that is, until Coug came along to create the first complex number to have a nonzero real part and a nonzero imaginary part.

-1/4 + i = -1/4 + i

Posted: Fri Aug 28, 2020 4:58 pm
Why stick to algebraic irrationals when there are so many more. Indeed, an operator is loosely defined; any function suffices. Thus came into being, this very weird constant, a number so strange and yet so fundamental.

arcsin(1) = pi / 2

Posted: Fri Aug 28, 2020 5:04 pm
Wheeee!

(-0.25 + i) + 256 = 255.75 + i

(I am counting (-0.25+i) as one number, and not two numbers, as it would be impossible to represent the number otherwise.)

Posted: Fri Aug 28, 2020 9:48 pm
Ircher noted the power of a unary function, and Coug nodded in agreement. Unary functions seemed the only way to get the most interesting numbers. And from this he remembered what he learned in college: the exponentiation function. And from this he could easily obtain the base of the natural logarithm:

exp(1) = e

Posted: Fri Aug 28, 2020 9:53 pm
256/2 = 128

Posted: Fri Aug 28, 2020 10:13 pm
While Ircher couldn't rip numbers apart, he could certainly join them together. Concatenation is an operation just as much as addition.

4 concatenated with 256 yields 4256

Posted: Fri Aug 28, 2020 10:18 pm
At last, after several numbers were made, it was time for dinner in the Universe of Numbers. There was half of a pi, but Coug still thought there was enough for everyone. There was, but as he multiplied a positive fraction by a negative fraction, Coug now owed the mathematical baker. That was good blueberry pi, though, and Coug began to color his numbers blue to celebrate how good it tasted.

(pi/2)(-1/4) = -pi/8

Posted: Fri Aug 28, 2020 10:32 pm
(pi/2) x 4 = tau

Who doesn't love a little Tau in their lives?

Posted: Fri Aug 28, 2020 10:33 pm
Wait, we can do 400 size now? I thought the max was 200...

With the natural numbers far from finished, Ircher sets out to count towards the sky.

2 + 1 = 3.

pedit: Tau? You remove that blasphemy right now!

Posted: Fri Aug 28, 2020 10:46 pm
tau / 2 = pi

Side note: Should we color code the numbers based on who discovered them?

Posted: Fri Aug 28, 2020 10:53 pm
Yeah, good idea.

pi / 3 = pi/3

Posted: Fri Aug 28, 2020 11:07 pm
3^3 = 27

Posted: Fri Aug 28, 2020 11:49 pm
Jumble, shortly after entering this world, grabbed the long bar known as "division" and the two nearest numbers. The resulting equation was...

1 / 0 = NaN

Oh, Jumble. You've done screwed things up again.

Posted: Sat Aug 29, 2020 9:05 am
"NaN?" Coug worried. "Jumble, are you trying to destroy this universe?" But then he remembered: 1/0, according to WolframAlpha, was complex infinity. He sat back and let Jake, the god of this Universe, be the judge, but for a moment he had a heart attack.

Then, as Coug walked across the complex plane, he noticed something lacking. There were three of the fourth roots of 1: 1 itself, -1, and i, all created by Jake. The fourth was curiously missing, but as it could be created from multiplication, it could be trivially added in: -1 * i = -i. And Coug saw that it was good.

Posted: Sat Aug 29, 2020 9:43 am
Jake seemed a tad upset that he didn't have ownership over all 4 units away from the origin. He decided that 1/0 would be the same as a complex number, or an irrational number, in that it would remain in original form, until it could be simplified.

i x pi/3 = (pi/3)i

Posted: Sat Aug 29, 2020 10:27 am
After pissing off the greatest god of the Universe a little in claiming the last unit away from the origin, Coug decided a little bit more teasing with Jake was in order. There were some numbers he wanted to create from trigonometric functions, but the argument he had created himself, so he could not do so. But, even though Coug had created e, Jake had now created (i*pi)/3, and now all it took Coug was to remember Euler's formula: e^(ix) = cos(x) + i * sin(x). Thus, Coug could kill two birds with one stone:

e^i*pi/3 = 1/2 + i*sqrt(3)/2