Numbers Theory # 2; Or, How I Won a Bar Bet. Plus, a Mystery.
I. First, the Mystery.
Does anybody know why every country and culture in the world uses the same numbers? As far as I know, anywhere you go on earth, regardless of the language spoken, everybody uses the same representations for numbers: 1, 2, 3, etc.
Why is that? How did a single number system get exported to every corner of the globe, but somehow without its accompanying language? We couldn't all have accidentally arrived at the conclusion to use the following symbol to represent one: "1", so how did everyone on earth get exposed to it?
My first guess was during the Roman Empire, when all of western civilization was unified and trading relations existed with the rest of the world, but then it occurred to me that Roman numerals (I, II, III, IV, etc.) are the only other number system I can think of, so that can't be right.
II. How I Won a Bar Bet.
Last night I was 0-1 on bar bets, so I asked my buddy if he was willing to bet a round on whether I could prove he was a God. Feeling the same way I do about friendly wagers (and probably feeling it was high time SOMEBODY noticed that), he accepted.
First, I asked if we could define being a God as an entity that can do the impossible. He said sure.
Then, I claimed it was impossible for non Gods to clap their hands. He objected. I asked him, "Isn't it true that before a person can clap his hands, those hands have to cover half the distance between them?" He said yes.
"And from that halfway together point, still before they can clap, don't they again have to cover half the remaining distance between them?" Yes.
"And again, before clapping, don't they need to cover half the remaining distance, no matter how small that distance may be?" He supposed so.
"And aren't there literally an infinite amount of these half distances that the hands must cross before they actually touch"? After some questions, he allowed that this was true.
"So for a mortal to clap his hands, he would first need to accomplish an infinite amount of tasks, those being to cross the infinite amount of half distances between his hands before they can touch, correct?" He's a gentleman, so he conceded the point.
"Is it possible for a mortal to accomplish an infinite amount of tasks?" Nope, it's impossible for a mortal to accomplish an infinite amount of tasks, at least without taking an infinite amount of time.
"I agree, watch." To demonstrate, I tried to clap my hands, where I brought them closer together while slowing them down, then essentially stopping just before touching, as they continued to cross the half spaces left between them without ever being out of a new half space to cross, before actually touching.
I said, "See, I can't do it. I'm no God." To that he readily agreed.
Then, smiling, I asked what happens when he tries to clap his hands. Being a good sport and generally fair minded dude, he clapped them.
"You've just done the impossible. By accomplishing an infinite number of tasks in the blink of an eye, you, sir, are proven to be a God."
Naturally, he whole heartedly endorsed that conclusion. But I was back to .500.
Well, hmmm, the thing with the infinite half distances is called Zenos paradox. The mathematical solution/explanation of/to Zeno´s paradox is taking the limit of ex. x approaching value y.
How come you did not know division by 0 was undefined, but know Zeno´s paradox?