He will think of a natural number, and you can have one guess at it each day. (Once he has thought of his number, he will never change it.) If you guess it, he'll let you out. Will you get out? (Remember - you have eternity...) Explain.
2006-08-18 05:17:27 · 20 answers · asked by amit k 1 in Science & Mathematics ➔ Mathematics
YES
The set of natural numbers is what we call countable infinite. This means that, even tough there is an infinite number of natural numbers, we know we could count them all (this will probably require eternity). The size of a set is called the cardinal number. For the natural numbers the cardinal number is called aleph-sub-zero, and it is the first transfinite number.
Now if the devil asked you to guess an irrational or real number then you would be in trouble. These sets are not countable, and there is "a lot more" than aleph-sub-zero possible answers. This means that you cannot count them all even if you have eternity.
2006-08-18 05:58:34 · answer #1 · answered by DarwinV 2 · 4⤊ 1⤋
There are unlimited natural numbers. Zero is sometimes a natural number and sometimes not depending on what u r doing. So lets assume the number is not zero. Now your job is to guess the number each day and see if u r right. There are unlimited numbers. U could guess "1" or u could guess "18,334" or u could guess "184,567,354" etc. This means that the odds on u picking the correct number each day are 1 out of an infinite number. This means that there is a never ending amount of possibilities so the odds approach but do not reach zero. Conclusion: It is theoretically possible for u to get out since u will be guessing for an eternity, but extremely unlikely that u ever will; also, bear in mind the devil will lie should u be right and then that will mean u have a zero chance and will never get out.
2006-08-18 05:27:21 · answer #2 · answered by Anonymous · 0⤊ 2⤋
the Devil will nid to think of a number, lets say x. If you have an eternity in hell, provided u dun die and that the devil doesn't cheat, by guessing 1 on the first day, 2 on the second, 3 on the third etc, you will be able to guess his no. in x days. But if he cheats, then you can never guess his number...
2006-08-19 22:15:52 · answer #3 · answered by MrYuQuan 3 · 1⤊ 0⤋
There's no range? I'd probably not get to leave, because there's an infinite number of, er, numbers that I could guess and still not win. In that case, the chance of me leaving hell would be infinitesimally smaller than winning the lottery, or getting struck by lightning. I'm screwed either way if that's where I end up, anyway.
2006-08-18 05:29:33 · answer #4 · answered by God's Honest Truth 3 · 0⤊ 1⤋
There is a chance, a distant chance, but the odds never change from day to day. Because you are there an infinite amount of time, and there are infinite natural numbers your chances at guessing stay the same.
2006-08-18 05:24:05 · answer #5 · answered by johngrobmyer 5 · 0⤊ 1⤋
Since he has to pick a finite value, say n, you just start guessing with 1, 2, 3. You will be out in n days.
2006-08-18 05:22:59 · answer #6 · answered by rt11guru 6 · 3⤊ 0⤋
Hell no, I can't even remember what natural number is!
Okay wait, I'm sure at least one of my math teachers will be in Hell with me so maybe I could torture them into solving the problem for me!
2006-08-18 05:22:56 · answer #7 · answered by siege 3 · 1⤊ 1⤋
YES.
If he keeps the bargain the number he picks will remain static. It has to be a natural number so you will eventually guess it.
2006-08-18 05:25:36 · answer #8 · answered by Anonymous · 0⤊ 1⤋
Screw that noise.. We all know he could cheat at that because the answer is in his head and he can change it, so I'd have to change the game. I'd probably have him zap up a PS2 and challenge him at tekken, super monkey ball, or sumthin like that.
2006-08-18 05:25:42 · answer #9 · answered by roknrolla 1 · 0⤊ 1⤋
Hmmm....
Well the probability of the event occurring, P(n), approaches 1 as n approaches infinity.
P(n) = n/infinity =~ 1 as n-> infinity.
Unless, of course, you are a Corky and keep guessing the same number...
2006-08-18 05:39:11 · answer #10 · answered by Anonymous · 0⤊ 2⤋