A Universe of Numbers. [Join Any Time]

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StrangerCoug
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Post Post #1  (isolation #0)  » 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.
Last edited by StrangerCoug on Sat Aug 29, 2020 8:48 am, edited 1 time in total.
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StrangerCoug
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Post Post #3  (isolation #1)  » 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.
Last edited by StrangerCoug on Sat Aug 29, 2020 8:49 am, edited 1 time in total.
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StrangerCoug
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Post Post #5  (isolation #2)  » 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 power—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.
Last edited by StrangerCoug on Sat Aug 29, 2020 8:50 am, edited 1 time in total.
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StrangerCoug
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Post Post #9  (isolation #3)  » 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 axis—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
Last edited by StrangerCoug on Sat Aug 29, 2020 8:51 am, edited 1 time in total.
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Post Post #12  (isolation #4)  » 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
Last edited by StrangerCoug on Sat Aug 29, 2020 8:52 am, edited 1 time in total.
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StrangerCoug
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Post Post #15  (isolation #5)  » 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
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StrangerCoug
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Post Post #19  (isolation #6)  » Fri Aug 28, 2020 10:53 pm

Yeah, good idea.

pi / 3 = pi/3
Last edited by StrangerCoug on Sat Aug 29, 2020 8:52 am, edited 1 time in total.
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Post Post #22  (isolation #7)  » 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.
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StrangerCoug
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Post Post #24  (isolation #8)  » 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
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Post Post #28  (isolation #9)  » Sat Aug 29, 2020 6:34 pm

Coug was always a clever number god. Earlier, he had sniped -i away from Jake, and now he was prepared to do the same thing with its angular phase.

-1 * pi/2 = -pi/2
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Post Post #30  (isolation #10)  » Sat Aug 29, 2020 6:52 pm

Coug realized that there existed what he needed to create the base of the common logarithm, having already created the base of the natural logarithm. All he had to do was change the operator in Ircher's most recent equation, though the creation of 7 and the pre-existence of 3 meant that there was another way.

2 * 5 = 10
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Post Post #34  (isolation #11)  » Sat Aug 29, 2020 11:13 pm

After a few back-to-basics number creations, Coug's thirst for more interesting numbers had come to resurface.

pi/2 / 3 = pi/6
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StrangerCoug
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Post Post #44  (isolation #12)  » Sun Aug 30, 2020 10:28 am

2^3 = 8

Now only one one-digit number remained to be created...
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Post Post #46  (isolation #13)  » Sun Aug 30, 2020 9:22 pm

Thus, any positive integer could, given sufficient iterations, be created simply by concatenation. But the next number wouldn't be so created—rather, Coug did a clever trick to do the exact opposite.

Re(255.75+i) = 255.75
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Post Post #48  (isolation #14)  » Tue Sep 01, 2020 4:33 pm

Coug gasped. Wasn't that against the rules? He could always create 11 himself, but keleven? Would Jake accept that as a number? He withheld his own powers until he had an answer.

10 + 1 = 11
Last edited by StrangerCoug on Tue Sep 01, 2020 5:19 pm, edited 1 time in total.
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StrangerCoug
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Post Post #51  (isolation #15)  » Tue Sep 01, 2020 5:23 pm

After Jake ate the keleven, Coug realized that he was hungry, too, so he got a little carried away and made a square pi.

pi^2 = pi^2

In post 49, Jake The Wolfie wrote:(Coug, if you want, you can edit your prev. message to add 11, or ask me how you want it made.)

(Done.)
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StrangerCoug
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Post Post #53  (isolation #16)  » Tue Sep 01, 2020 7:36 pm

Among the Greek letters that existed, there were pi and tau. Now there would be zeta(2), though that being a function with a number Coug had already created as a sole argument, he couldn't directly use the function. However, he knew what the function would output:

pi^2/6 = pi^2/6
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Post Post #58  (isolation #17)  » Tue Sep 01, 2020 9:38 pm

"Square roots of square roots?" Coug asked. He saw that, by simplification, the square root of the square root was the fourth root, and the square root of the square root of the square root was the eighth root. But why did the root have to be a power of two? Odd roots had the power that taking one of a negative real number gave another negative real number.

cbrt(-3) = -cbrt(3)
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Post Post #60  (isolation #18)  » Wed Sep 02, 2020 11:47 am

(That's actually the common log of 10. A valid number, but not the base of the binary log xD)

Complex conjugate of (255.75+i) = 255.75-i
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StrangerCoug
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Post Post #64  (isolation #19)  » Wed Sep 02, 2020 8:04 pm

In post 62, D3f3nd3r wrote:"Lg" is the common log?

Idk I'm an engineer, so "log" is common and "ln" is natural

(Just plain "log" is ambiguous and depends on the context you're talking about. That's why the symbol lg (without the o) was devised.)

Im(65404.0625-1023i) = 1023
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Post Post #70  (isolation #20)  » Thu Sep 03, 2020 12:21 pm

Modulus of 1024+1024i = 1024*sqrt(2)
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Post Post #72  (isolation #21)  » Thu Sep 03, 2020 9:08 pm

(You technically need the parentheses around my entire number before squaring it or it'll be 2048, but I get you.)

log_2(2097152) = 21
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Post Post #74  (isolation #22)  » Mon Sep 07, 2020 6:33 pm

Who would have known that an imaginary number to the power of an imaginary number would be a real number?

i^i = e^(-pi/2)
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Post Post #79  (isolation #23)  » Tue Sep 08, 2020 9:29 am

1/(e^(-pi/2)) = e^(pi/2)
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