Well done. 
I’m afraid that that web page is not in english. Care to translate?
Because I would be very interested to know exactly what the finite number of flips is that you can do before your axiomatically fair coin becomes unable to land on heads.
Yeah — but 3.243F is all you need, most of the time.
In previous eras, thinking on the topic has been dominated by ignorance and superstition, but we live in an age of reason, where the question of monkeys at typewriters has been put to a rigorous scientific test.
But now someone has attempted to put the theory to the test. Admittedly the British academics involved in this unusual project did not have an infinite number of typewriters, nor monkeys, nor time, but they did have six Sulawesi crested macaque monkeys, and one computer, and four weeks for them to get creative.
The results of this trial at Paignton zoo in Devon were more Mothercare than Macbeth. The macaques - Elmo, Gum, Heather, Holly, Mistletoe and Rowan - produced just five pages of text between them, primarily filled with the letter S.
There were greater signs of creativity towards the end, with the letters A, J, L and M making fleeting appearances, but they wrote nothing even close to a word of human language.
“It was a hopeless failure in terms of science but that’s not really the point,” said Geoff Cox ,of Plymouth University’s MediaLab, who designed the test. So what were the academics trying to achieve? “It wasn’t actually an experiment as such, it was more like a little performance,” said Mr Cox.
The project - which was paid for with £2,000 of Arts Council money - was intended to emphasise differences between animals and machines, he went on. “The monkeys aren’t reducible to a random process. They get bored and they shit on the keyboard rather than type.”
but some very strange things could happen in an infinite universe, if we allow events with very low but non-zero probability to occur. Quantum fluctuations might allow a random object like an elephant to appear, or disappear, or jump ten metres to the right; these events would happen very rarely, even in an infinite universe, but they could happen.
Somewhere out there there might be an exact copy of our Hubble volume where some very strange, random events are occuring, or are about to occur.
Who knows, we might be in one of them.
This may be a stupid question, but do we know for sure that the physical law we know of is the only possible set of physical laws possible in existence (in the very broadest sense)? I mean we really can’t say how our universe with it’s physical laws came to exist in the first place, how something came from nothing, or if it did. Maybe our universe will be dead someday and another big bang type event creates something entirely different and unimaginable to us.
Am I thinking too far outside the box?
You have a point - and it would be really freaky to transition from an area with one set of natural laws to an area with a different set. (Well, freaky or fatal.)
I believe that logical laws are a bit more reliable regardless or when or where you are, Schroedinger’s cat notwithstanding.
I certainly hope the OP is true. I am looking forward to my 3-way with Ashwarya Rai and Rebecca Romijn,
While I wait, I’ll be in my bunk.
Oh… make that a 4-way and throw in Kate Beckinsale.
If my OP is true then you already have. Congrats:)
If 0.999999(forever) = 1 they why isn’t something infinitely approaching zero not equal to zero?
If you keep flipping the coin the chances it will keep landing on one side are infinitely small. Why isn’t that the same as saying the chances are zero it will happen?
There is no such thing as a “completed infinity.” The odds never actually reach zero; they only approach it to within any specified nonzero difference.
(Charles Dodgson, more familiar to most of us as Lewis Carroll, didn’t comprehend this vital principle of the infinitesimal calculus! Martin Gardner, in one of his Mathematical Games columns, quotes Dodgson as complaining that the concept of “limit” doesn’t work, because it doesn’t eliminate the difference, but always retains some small nonzero difference.)
You cannot possibly flip an “infinite” number of heads (or tails,) because you will never actually flip an infinite number of coins in the first place!
Because infinity isn’t actually a number. There are those that will disagree with me on this.
But as you approach infinity, it’s possible to do this without actually getting there, which is met with less disagreement. The reason for this is that something that is infinitely approaching 0.999999(forever) hasn’t actually got there, and never will. Illustration follows:
Consider a process why which you take your number and add another nine after every step. So at step 1 the number is 0.9, at step 2 it’s 0.99, at step 3 it’s 0.999, and so on. At step 100 it’s 0.9999…999 out to 100 nines - but no further (yet). Keep repeating this unchecked; forever, if you will.
So you do this forever, and you do indeed end up with an inpressive number of nines. But at every single step along the way, it’s still a finite number of nines, because you have only gone a finite number of steps. This is true even if you do this forever, becuase you never run out of finite numbers; there’s always one more. And so because you never pop off the end of the number line, you never actually get to that magic number that floats somewhere off it’s end, inifinity…because you never get to and end at all. There isn’t one.
Summary: You can count “to inifinity”, but you never actually get there; ‘infinity’ is a direction, not a destination. And similarly you can get infinitely close to 0 without ever arriving.
ETA: What Trinopus said (and said better).
I may be talking straight out of my arse here, but IIRC, this has to do with the way the limit of Cauchy sequences (sequences where the elements grow arbitrarily close to each other) is calculated. It is similar in nature to the conundrum of infinite series of non-zero elements that do not diverge, in that a sum of infinitely many non-zero elements intuitively should be infinite, yet very often is not.
Contrary to what one poster (I forget who, and for that, I apologize most insincerely) proclaimed, the concept of infinity is understood in excruciating amounts of detail by mathematicians. That ye of limited mental acumen fail to understand transfinite cardinality and other such concepts does not mean infinity is a vaguely understood concept! 
Damn! How could I have forgotten that?
So… Demonstrably, the OP is not true. I’ll still be in my bunk.
The problem here comes from conflating limits (as x approaches 1 it goes though 0.9, 0.99, 0.999… just keep adding 9’s) with the actual number 0.9999…
The repeating 9’s aren’t getting any “closer” to 1. It’s a fully formed number that simply “is”, and the repeating 9’s are an artifact of decimal notation.
Think of it like this.
(1/3) + (1/3) + (1/3) = 1
1/3 = 0.3333…
so (0.3333…) + (0.3333…) + (0.3333…) = 1
0.9999… = 1
No limits, no movement of the number, it just “is”.
I have a friend who is a fierce “constructivist.” He insists that a “number” must be constructible, by a finite and algorithmic process. A recipe that a person could actually follow manually.
Thus, somewhere along the line, as 0.99999… gets longer and longer, there comes a point, a finite point, where, according to this strict constructionist view, it stops being a number! He can’t tell us where, exactly, but somewhere, perhaps in the low hundreds, that long string of nines “stops being a number.”
He rejects any proof that involves infinity, since infinity, in any of its forms, cannot be constructed. He rejects the proof that the square root of two is “irrational.” To him, all numbers are rational. There are no “real” numbers, in the sense of numbers like e or pi that can’t be constructed.
A fascinating side-step into an alternate philosophy of mathematics.
(Of some interest, too, to students of psychology…)
As Norton Juster wonderfully put it in “The Phantom Tollbooth,” “Follow that line forever, and when you get there, turn left!”
But aren’t you doing the same with the coin?
Yes there is the actual flipping of the coin but we can model it mathematically and come up with a number that just “is”.
As mentioned I cannot actually perform an infinite number of coin flips. However, if I ask, “What are the chances of getting all heads on an infinite number of coin flips” I assume the answer would be “infinitely approaching zero”.
Alternatively, imagine I perform a calculation that comes up with an infinite series of .99999… I keep doing the math step by step and keep putting another “9” on the end of my string of nines (akin to me flipping a coin over and over again).
How is that different than what you proposed? If 0.99999 is never quite “1” but deemed to be one how is forever approaching zero but not quite zero not in the same boat?
Think of the universe as a box full of red, blue and green colored marbles. Given a large enough box, the same pattern of r,b,g is likely to repeat. The gist of that theory is there are a finite number of types of molecules and they take a finite amount of space, just like a big box of marbles. So theoretically, you could have another configuration of molecules that matches you or even an entire planet that happens to be exactly like Earth some distance away. Unfortuantely, that distance is several orders of magnitude further than the edge of the known universe. But theoretically possible.
Technically it could be in the next star system over but yeah…chances are it is nowhere near you.
My old Calcs teacher said to think of it as two guys arguing a case before a judge. You name a number, greater than zero. Any number you want. I can, quick as a wink, respond with a counter-offer, which is less than your number, and yet also still greater than zero. You put forward 0.25; I respond with 0.2. You put forward 0.0002; I’m happy to respond with 0.00002. It’s a game you cannot win; no matter what positive number you put forward, I can successfully put forward a smaller positive number.
Now: can you put forward a number that is between 0.999… and 1 (non-inclusive)? Go ahead and try; I will put forward a number that is also between 0.999… and 1, which is closer to 1 than your number was. I can always do this.
There is, also, one further small difference. The notation of (say) 0.3333… for “1/3” is really only a matter of convenience, given that some people prefer a decimal expansion as an issue of style. Here, the number 1/3 has already been constructed. We aren’t attempting to construct 0.33333… by a process of adding more 3’s.
We could do this, of course. Sum over n for 1 to infinity of 3/10^n. This is a process that has a limit of 1/3. But we don’t have to do it that way, as, for instance, we pretty much have to for e or pi. We can’t construct e or pi, but 1/3 is a very, very simple construction.