There's a possibility that any given molecule can phase through it. You comprise a finite number of molecules, so therefore the probability of your whole body going through is nonzero, albeit extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely extremely tiny.
I suppose that is true, maybe, but quantum mechanics only work on the quantum level - that is, at the point when particles begin to break down into wave functions. Not only would you have to take into account the incredibly, astronomically small probability of all the particles in a body going through a quantum tunnel and ending up intact and in the right order on the other side, you'd also have to account for the particulate forces working against that.
I am the kind of person who thinks 0.9 repeated does not equal 1, at least not mathematically, but in this case it's so damn small (0.01 with a repeated .0) I have to disagree that it's possible within our finite universe.
.999... does equal 1, and for some reason I'm going to drop the proofs on you.
1/9 = .111...
3/9 = .333...
8/9 = .888...
9/9 = .999... , or 1.
Same proof applied to 1/3
Not only that, but in the set of the reals, no number can be placed in between .999... and 1. Any number you think can be placed (like .000...001) can't, because if it can, the number is not infinitely trailing like .999... is, or the .999... in question is not infinitely trailing like the actual number should.
There's even that x thing, that is an actual accepted reason of .999... = 1.
x = .999...
10x = 9.999.... (This can be done due to Hilbert's Hotel paradox)
10x - x = 9 (Here it's assumed that you know that 9x = 9, so common division gives the next line)
x = 1
Other proofs are hard to show here without LaTeX, but I do believe numberphile made a video on this.
Seriously, it's not even discussed anymore besides by flamers on /sci/.
3/9 is not equal to .3 repeated. No matter how far you go it's always short one third of 0.01 with a repeated .0 - This is not a full proof. (On a related note, that's why you typically get 0.3333334 in decimal calculations of one third)
The 10x - x concept is definitely solid, but it's not changing my opinion. No matter how much proof you give me, my belief that .9 repeated will always be asymptotic to 1 is unchanging. In practicality, of course it is equal to one - there are not infinite divisions to make, unlike in mathematics.
www.wolframalpha.com/input/?i=1%2F3
You can even do long division to see that a 12 digit calculator is just simplifying it for you, and typically it rounds 2/3, or 6/9-8/9 up to .6667, .7778, .8889, respectively.
I'm not going to thumb you down or anything, but I feel as though someone might. Just headsing you up.
"3/9 is not equal to .3 repeated. No matter how far you go it's always short one third of 0.01 with a repeated .0"
You stated this as the reason why it shows up as .3333334, which when written shorthand, is "Wrong", or ".3333334 is the typical and the correct result, AND this is why it shows up."
And actually, it technically does NOT equal 9.999..., as .999... times 10 equals 10, since .999... equals 1. 1*10 = 10. www.wolframalpha.com/input/?i=.9+repeating+*+10
I feel like you aren't clicking on these links I'm giving you.
I only meant that calculator programming accepts or implies that 1/3 is a little bit more than .3 repeated. If it didn't, then it would round down to .3330 or just end the string with a 3, as opposed to rounding up and ending it with a 4, when presented with a decimal of one third. This does not entirely constitute my beliefs, it was just made as a related comment.
I have clicked on all two (2) of those links.
Also, my math final is at 3:30 today, so thanks for making me think about this stuff. But, unfortunately, I do not have to calculate thirds or dispute the meaning of .9 repeated. So I'd better get back to the actual review.
Actually, scratch that; I don't think the 10x - x is proof of .999 repeated being equal to 1, unless you can provide proof that 9.999 repeated is in fact ten times 0.999 repeated.
people are evolved monkeys. there was a decidedly finite (but very large) number of them that have in fact written every Shakespearean drama (whether or not they were written by one person/monkey or not). rewritten them..adapted them to movies and/or tv shows..and now even discussed them on funnyjunk. is that irony? or justice? im not sure.
Actually, there's a school of thought that if you took an infinite number of monkeys and gave them each a typewriter for them to randomly bang on, eventually one of them would have a perfect copy of Hamlet. But nice try.
According to those laws, it is likely to happen. Doesn't mean it will.
Also, you completely fail to understand that just because there is one infinity doesn't mean it isn't cancelled or otherwise nulled out to a finite number by another infinity. If that's the case, then it's not even necessary for it to be likely to happen, and it may in fact be the case that's it's likely to not happen (******* surprising **** that, isn't it!)
and here again we reach the brick wall where the mammalian brain stops and the actual universe starts. is anything actually infinite? or is it simply a term that we have invented..like zero. I follow a blog where many folks much smarter than me..many highly educated math folks believe that numbers are discovered and not invented. they point at magical primes and the Fibonacci numbers...there are scores of jews converting texts into numbers as we speak. they even have a biblical book dedicated to numbers. numbers have power. names have power...but in the end, it doesn't even matter. - good charlotte
No, that's not how it works. Infinite cycles mean that it converges to a probability of 100% but never reaches it, so there is still a chance that it will never happen
No that's not how it works. As the cycles converge on infinite the probability converges on 100%. If the number of cycles actually is infinite and the probability of it occuring in one cycle is greater than zero then it will occur.
You are correct, but I'm pretty sure that it is so infinitely close to 100% that it is considered to be so, sort of like how 2^-infinity is so infinitely close to 0 that it is considered to be so. In the end your correctness is correct (makes perfect sense) because there is no applicable infinity making the whole thing irrelevant. Truth is, I'm just rambling on and have no idea what I'm talking about. Also, why is there no infinity symbol on the keyboard?
The problem is everybody is not thinking about the problem correctly. Many of you are trying to think about what happens if the number of cycles is impossibly large, say 99999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999. However this is no closer to infinity than 2 cycles is. Infinity has no end, it is not a set number so even if after an arbitrarily huge number of cycles where the event doesn't occur there are still infinite cycles to go where it can.
Actually there is an infinite symbol: 8 hue hue But seriously, infinity can be a bitch. If we assumed that it will actually happen with a probability of 100% it would mean that it will happen an inifite amount of times. But it will also not happen a few times. I'd like to explain it a bit better, but english isn't my first language. Also it's late here I should go to bed now.
Also, according to that law, you should be able to drop 100 oranges off the empire state building at the same time and have them land in 10 perfect parallel rows of 10 and unharmed, but the chances are so miniscule (10^50+) that they throw it into the 'impossible' category.
is it 10^50+? or is it 10^-50-? if the exponent is negative it will turn into a fraction and get extremely small, but if its positive then there is an extremely high chance of it happening
ok yes if its 1 in 10^50+ that would make sense, but if its a 10^50+ percent chance then it would be happening all the time and if its a 10^-50- percent chance then it would be a very small fraction