Does True Randomness Actually Exist? ( ^&*#^%$&#% )

But in binary that's 0.111111... and @Optimissed says that's impossible. Or at least it must terminate.

To be serious, yes. Mathematics is generally not an optional abstruse way of doing things: it's the only way that makes sense of them.

You might be interested in the way infinity entered a different discussion. Discussing solving chess, I was considering a basic variation of chess where there was no 50 move rule or any repetition rule. This is not technically a combinatorial game because games can be infinite, in principle. So theoretically you can permit this possibility and define a game that never ends to have the value of a draw. This makes the game theoretically very like ones with at least one drawing rule that prevents infinite games - the rules are there to stop it being possible for play to go on forever.

If you attempt to enter 0.111... on a really big calculator, eventually your finger will slip and hit "2" by accident, which will terminate the series, QED.

yeah endless means just that.

Infinite Definition & Meaning
 
1 : extending indefinitely : endless infinite space · 2 : immeasurably or inconceivably great or extensive : inexhaustible infinite patience · 3 : subject to no ...

Unfortunately, you must be completely wrong on those three points, since you say "Elroch is completely wrong" and he agrees with you.

Suppose we say the experiment is to flip a coin an infinite number of times... if we repeat this experiment an infinite number of times (that is, a infinite number of infinite coinflips) then you're saying every possible outcome will happen... meaning that in at least one of the experiments flipping all heads will happen.

Yes.

Actually just a little idle amusement.

The blunt version is that you lack anything close to the standing to judge my posts. You lack the expertise and have a habit of sloppiness and inaccuracy.

Do you prefer that?

So given the equal chance of any outcome (symmetry w.r.t. swapping heads and tails for any flip, or any set of flips), why is it that that outcome cannot occur while some other can occur?

Actually, do describe an outcome that can occur. There have to be some, right?

(Unfortunately, this is an example of you not really having the understanding to contribute to a constructive discussion. The problem is that you are not psychologically disposed to develop that understanding. I have now tried to lead you to understand that there are no impossible sequences several times, but you have chosen not to improve your understanding)

I understand that your ego is strangely reliant on some sort of belief in high general intelligence that most have lost interest in as teenagers, as they moved on to real subjects, but it is wise to remember that this is just a useful technique for determining the potential of children. What matters for adults is applied intelligence, expertise in a specific topic. General intelligence still plays some role in the capability to develop such expertise, but it is obviously no replacement for doing so!

It's worth noting that the number of possible infinite sequences of binary outcomes is uncountably infinite. A countably infinite number of repetitions scarcely scratches the surface of the possibilities. It is easy to prove that the probability of what is omitted is 1 (a countable set of sequences is a union of a countable number of sets each of which has probability 0).

In calculus, infinity is always correctly dealt with using limits and sets of statements about finite things.

As a simple example, the integral of 1/x from 1 to infinity is known to be positive infinity (using the extended real number line). What this means is that tbe sequence {I(n)} of integrals from 1 to n grows without bound as n increases.

More precisely:

Given any real number B, there is some n(B) such that for all m > n(B), I(m) > B

(a set of statements about finite things, as mentioned in the first paragraph).

So you can view infinity as a shorthand for such statements.

You can also extend the arithmetic of the real numbers to include pseudonumbers +infinity and -infinity, but some results (eg +infinity + -infinity) are necessarily undefined.  The results that are defined can be justified as statements about limits like the above that do not explicitly involve infinity, so here too infinity is a shorthand.

Your statement that an infinite run of heads is "impossible" is exactly as misguided as saying the decimal number 0.7777... = 7/9 is impossible.

ALL SPECIFIC SEQUENCES OF OUTCOMES (INCLUDING AN INFINITE SEQUENCE OF HEADS) HAVE ZERO PROBABILITY. ALL ARE POSSIBLE BY DEFINITION.

Was the fifth attempt to communicate that loud enough to hear?

You lack intuition about probability measures on uncountable domains (such as the set of all sequences of coin flips). Intuition from finite, discrete probability spaces does not extrapolate.

If it helps consider the uniform probability distribution on the unit interval [0, 1] (another uncountable domain).  The probability of any specific number in the interval is zero. All numbers in the interval are possible, by definition.

 I know true randomness exists because I can't match 1 powerball # in 30 yrs.                 

You seem to think he's making stuff up, but this quote (in caps) is not a controversial statement. In fact it's a fundamental part of any continuous probability distribution i.e. it's fundamental that each event in such a distribution has a probability of zero, but each event is possible

(and together all probabilities sum to 1, meaning something will happen, but since there are infinitely many, each individual event has zero probability).

And anyway, repeating an infinite event an infinite number of times is not rendered invalid by saying "there is only one infinity." Since the objection doesn't mean anything it's hard to address other than saying that.

Keep trying, you're bound to get it eventually... right?

In #3918 you said "Infinity allows anything that can happen to happen"

So you already agree that all heads will happen if the expriment is repeated an infinite number of times.

There is no rule or law of physics or etc that says a coin can't land on heads in the next flip if it has landed on heads __ number of times in a row.

Yes, there are different types of infinity, some larger than others. Cantor's diagonal argument is maybe the best known example of proving a difference exists between countably infinite and uncountably infinite, and occurred in the 1800s.

Maybe some other civilization came to the same conclusion earlier, but had their libraries burned by invaders, who knows

It's a simple enough idea, so very believable if someone told me that it had been thought of 1000s of years earlier.

Lmao this ego DRAB is BEYOND RIDICULOUS