So my mate comes over and drinks MY piss, right, and says "y'know" he says, "the hare will NEVER catch the tortoise. Ever."
I says "pig's arse" and he says "nope let's say the hare runs ten times faster, and the tortoise has a ten kilometre head start. They take off TOGETHER, so the hare runs 10km to the tortoise, but in that time the tortoise, at a tenth of the speed of the hare, has gone another km. so the hare goes another km, but the tortoise has gone another 100m. So the hare goes another 100m, but the tortoise has gone another ten metres. So no matter how many times the hare keeps going to catch the tortoise, he slow bastard has ALWAYS gone a tenth of that distance and therefore will never be caught."
After stewing for an hour or so, I told the f&$@tard he was full of ****, coz even though the gap became infinitely small, he was ASSUMING that 0.99999999 recurring was NOT equal to one, ie the gap remains finite. He says of course it doesn't equal one you ****head, but I says hang on knob jockey, if 1 minus x = 0 then what is x? He says 1. Yeah. Now what is 1 minus 0.99999999999999999999 etc???????
Now it CAN'T be 0.00000000000000 etc etc with a one on the end because then it becomes a finite number, so it must have infinite zeroes and therefore never get the one on the end, therefore it equals zero, therefore 0.99999999 etc equals x equals one and the furry little bastard catches the tortoise, and takes off into the sunset.
I think.
So who is right?
I says "pig's arse" and he says "nope let's say the hare runs ten times faster, and the tortoise has a ten kilometre head start. They take off TOGETHER, so the hare runs 10km to the tortoise, but in that time the tortoise, at a tenth of the speed of the hare, has gone another km. so the hare goes another km, but the tortoise has gone another 100m. So the hare goes another 100m, but the tortoise has gone another ten metres. So no matter how many times the hare keeps going to catch the tortoise, he slow bastard has ALWAYS gone a tenth of that distance and therefore will never be caught."
After stewing for an hour or so, I told the f&$@tard he was full of ****, coz even though the gap became infinitely small, he was ASSUMING that 0.99999999 recurring was NOT equal to one, ie the gap remains finite. He says of course it doesn't equal one you ****head, but I says hang on knob jockey, if 1 minus x = 0 then what is x? He says 1. Yeah. Now what is 1 minus 0.99999999999999999999 etc???????
Now it CAN'T be 0.00000000000000 etc etc with a one on the end because then it becomes a finite number, so it must have infinite zeroes and therefore never get the one on the end, therefore it equals zero, therefore 0.99999999 etc equals x equals one and the furry little bastard catches the tortoise, and takes off into the sunset.
I think.
So who is right?