but... the bird is the word...
so what came first the chicken or the egg?

This post was edited by guywhosebrother on Nov 17 2012 04:30pm

Something having a chance of 100% does not guarantee that it will happen. To prove that let's use the inverse real quick. Lets take something that has statistically 0% chance of happening but still happens. Also let me clarify that the following does not have an almost 0% chance of happening. It is actually 0%.

Ok so bill is told to pick a number. It can be any number at all.

Now Fred is told to pick a number. He has the same requirements and he does not know what number bill has chosen. So what is the chance of Fred picking the same number? It's 1 over infinity aka 0%. Here's the kicker though. There is no rule, law, theory, hypothesis, or other logical struct that bars him from picking the same number so it can happen.

Now let's go the other route. Lets say you have a "fair" coin. The chance of you flipping heads is 1 / 2. The chance of you not flipping heads after x flips is 1 / 2 ^ n where n is the number of flips. (I can prove that algorithm mathematically if you wish). So let's say you flip the coin infinite times. Yet again the chances of not flipping becomes 0% or stated another way the chance of you flipping heads is 100%. Now what physical law or principal says that you can't flip tails infinitely in a row? There isn't one, and because it is a possible outcome it can't be ruled out. This means that things can be a statistical certainty and still never happen, not even on an infinite timeline.

can you explain how you got to 1/infinity %?

when something has a 1/infinity chance of happening, on an infinite timeline, it has a 1/1 chance of happening.

sorry
1/∞ * ∞/1 ≠ 1

The odds of getting 0 heads after:

1 throw: 1/2 = 50%
2 throws: 1/4 = 25%
3 throws: 1/8 = 12.5%
10 throws: 1/(2^10) = 1/1024 = 0.098%
infinite throws: 1/(2^infinity) = 1/infinity = 0%

right i understood the limiting process on the coin flip one...i'm confused by the picking random numbers scenario

the coin flip one bugs me because it abuses the idea of infinity as a number. the physical law or principle that says you can't flip tails infinitely in a row is that there's no such thing as an infinite quantity...infinity isn't a number

This post was edited by Derkaderk on Nov 27 2012 12:41pm

well then how about: as the number of coin flips approaches infinity, the probability of getting 0 heads approaches 0

This post was edited by Azrad on Nov 27 2012 12:59pm

When bill picks a number let's assume he chose the value 3.9621432. Now it's fred's turn to pick. He has an infinite number of choices. He can pick any number whatsoever. So the chance of him choosing bill's number is 1/infinity aka 0, BUT it is possible for him to choose the value 3.9621432. In science they call this scenario "Almost never" which means there is a statistical chance of actual 0% but it can still happen. Almost never is the exact opposite of "almost surely" which means it has the statistical chance of 100% but may not ever happen (which is the case for those air molecules).

I think for all intents and purposes, in this thread you can assume that when we're saying "infinity" we actually mean "the limit as x approaches infinity".


Actually in statistics if you have a continuous probability distribution, then you can calculate the probability of choosing a value within a range of numbers through integration. If you try to integrate between a range of 3.9621432 and 3.9621432, then no matter what the probability distribution is, you're going to calculate a probability equal to zero.

Edit: the textbook example of this scenario is "What time will the mailman arrive to pick up the mail if you know he shows up between noon and 1pm?" The probability he will arrive at exactly 12:30pm (and 0 nanoseconds etc...) is exactly 0, but the odds he'l arrive between 12:30pm and 12:31pm is a non-zero number. Calculus-based statistics was a fun course, haha

This post was edited by bentherdonethat on Nov 28 2012 10:01am