Count to N
Natural number (N) - the set of non-negative integers {0, 1, 2, ...}; set is countably infinite: it is infinite but countable by definition.
There is a natural number 0.
"Zero" was nothing but a jar. Jar with clean, definitely natural DNA-packed substance. Pure essence. An organic, primal soup of life. The colour of neon light shimmered against the slippery glass surface when he skimmed gloved hand against it. The very essence of his creation which had no colour.
He lifted that jar and spilled its contents into a big test-tube. Its density was far from water's. Appearing like a giant ball of clear mucus, it slid from the jar and, with plop, entered the new environment, completely different than the small, sterile and cosy jar of glass. It swam, no, it soaked in, reaching the tube's bottom and then flowing up to where the pressure seemed to be stable – to the centre.
Every natural number a has a natural number successor, denoted by S(a).
Number 1 was a failure. Where he found "Zero" to be a great progress in itself, the next number was a complete and utter failure. Combined DNA with one he got from the Little Princess, something causing immunity and strong, nice growth. Now it was in even worse state than "Zero" was. "Zero", by the way, wasn't swimming, but existed peacefully in its centre of test tube and seemed to be content. It had a week and he could already see some one or two cells around the primal blob. Well, not all was lost. He poured acid into the test tube with 1, and the cat-dog-whatever foetus-like, highly deformed thing dissolved quickly. He didn't even note down its existence.
Intuitively, S(a) is a+1.
New number 1, came to be more stable, but it still wasn't the effect that he wanted to achieve after three long months of brainwork and two weeks of waiting for its effects. It came out weak and didn't last more than few hours in a tube. At least it had a human form. Beautiful form. But with no brain, just highly-concentrated neural tissue here and there. Mostly in places he didn't know a neural tissue can get into. Noting the progress on pad, he already got the idea how to place the brain where it should be. And develop artificial respiratory and maybe circulatory system, if necessary. Everything was so messed up, but slowly he will get to it. He also noted new development in "Zero". Few bigger cells began to pulse rhythmically, filtering the water from nutrients. He will have to change biologically neutral filling into something more like amnion fluid. Smiling to himself, he patted his plush companion that always followed him, before getting back to his work and, most importantly, getting rid of unnecessary "new" 1.
There is no natural number whose successor is 0.
Number 3 stood silently against one of the life-supporting machines that the man in white thing invented for him. 3's presence was known about, but he was ignored. No one who mattered and now the white man was running back and forth from the desk and something that looked like a big metal table. The another was laying there and now that one seemed more important. Four days before, he was the one and only who laid on that table. The man in white was working hard on another since yesterday. Didn't even have time to change 3's drip, so the cord dragged blood into itself, causing all his left arm to turn purple. The man was very unhappy then. He was running so fast, his face seemed askew and his lips crooked. His whole body moved in angry, fast way and 3 didn't know why. He couldn't ask as he couldn't move from the basement. The all machinery was too heavy to move it anywhere and the lift wouldn't do. It seemed to cause the white man to become irritated more lately.
The another moved all of sudden and man in white appeared right beside him, his lips moving eagerly. There was a big 4 on another's arm that he'd just noticed. 3's sight was getting worse and worse every day. Something was wrong with it. Something was wrong with 3 and the man in white knew it well. Another's mouth moved then, through the move was slower than man's. Cords that connected 3's body with the various instalments shook as he shivered. Grabbing at the pipe, which linked his trachea with the weird machine, he closed his eyes sadly. 3 was incomplete. 3 was a badly made replacement. And 3 just got to know why…
His first good creation was able to stand mostly by itself. Moved, had face mimicry, could even smile back. Its brain's cortex's responses were great. Retinal detachment showed up and its veins got obstructed by blood fast. It seemed intelligent, almost like a two or three-year-old. Deaf-mute though. He noted every single thing in his notepad, added his comments, all machinery's record data. He even grew fond of that creature though. A year of work just wasted, one could say.
Its mental and physical state deteriorated hour by hour. He spent a long time preparing the right dose and contents of anaesthetic to make him go.
It was the first one who looked just like that man.
S is injective, i.e. distinct natural numbers have distinct successors: if a ≠ b, then S(a) ≠ S(b).
If you knew what would happen, you'd never go away the way you did.
There would be no broken vows, no broken mirrors, no broken glasses. No hands wrapped in cotton bandages, no cursing the gods. There would be faith.
"You have no God here, do you?" - "Not anymore, I think."
One after another I had to put them all down. They all looked at me and smiled, you know? Would you smile as well? I doubt. You had other, you thought "brilliant", idea. Something better than living for me.
Now look what happened. Look what is going to happen. It's all your fault. Enjoy the show, Moon.
If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all natural numbers.
- What's my name?
11 asked one day. All of sudden, without any purpose. Did his memory disc fail?
- Eleven.
- What's my real name?
That question struck him. Shocked, he looked from above the laptop screen flashing various data about "Zero's" stable development of all internal organs.
It appears that something slipped from his hands and it seemed to be consciousness and self-awareness of his projects. The first page in folder about 12 was soon to be ready and here comes 11 asking such questions, denying his very own existence as a test subject. Making him something close to a human.
Nii didn't answer.
- What was his name, then?
…