Creek piszed down his leg again. Obviously he never took calculus in civul engunear skool. Or else they dumb it down for engunears.
The value of a function or process at infinite tries is the evaluation of a limit to infinity. For a limit to infinity to exist the output value must get ever closer to the limiting value as the domain value increases indefinitely.
His hypothesis that a coin toss summed up and carried to infinity must always equal zero violates the common understanding of a limit to infinity. There is no such thing as 'infinity' by itself if one cannot understand that some quantity is approaching a constant as you go that way.
The RMS distance from zero for the coin toss sum grows as the square root of the number of throws. Carried to infinity the RMS distance is infinity and the probability of the sum being zero at any particular stopping point goes to zero. Exactly the opposite of his idea.
He is confused about the difference between the outcome of a single experiment carried on to infinity and the average value of the experiment when each end result is averaged an infinite number of times.
But he is a scientist... LOL !!!!!
On average the sum will be zero but any particular run even to infinity will NOT. What ya got next.. Enjoying this immensely.
""Why bother mentioning infinity""
Because you made the moronic mistake of claiming that the coin toss carried to infinity would with certainty sum to zero.
Why you said such a stupid thing I don't know but it is sure fun to push it up in front for all and you to see.
Yes if you notice for the definition of taking a limit to infinity the fact is that one more step breaks the convergence then the limit does not exist. The same answer came from the math stackexchange post.
Dum Dum dum you are.
Well guess is about all you can do. Yes I am asking to take finite milestones to infinite question, which is not silly it is how limits to infinity are determined.
If a function has a limit at infinity , say L, then that means that as the independent variable grows the function moves ever closer to L. I don't think you took any calculus. But then rock digging doesn't require it.
Try using google to help yourself. Search "limits to infinity" and see if you can understand. Gawd this is such fun, cutting down the board know it all with something he cannot BS about.
a series of zero mean random variables are summed up to time T.
Obviously the expected value of the sum is zero. Or put another way the average value of this sum will be zero.
However the expected value of the sum squared is not zero for any time t greater than zero.
In fact the expected value for the sum squared grows with t proportional to the square root of t.
Taken to infinity is there a point where the expected value of the sum squared trends back to zero.
Or equivalently is there some point where any particular run of the sum would grow as t increases
and then begin to decline toward zero with increasing t. If so where does this transition from rising
to falling happen.
The simplest differential equation known to man has the form
Dee Y over Dee x equals minus alpha times x. An example from this class is given by.
If Y equals 81.6 at x equals 20 and Y equals 132.3 at x equals 40
what is the limiting value of Y.
Worth fighting Russia over..
Wow your gun and oil friends must really be itching for some new cash. Undertakers as well.
But.. didn't you say previously there had not been any warming in the last decade...
Did you not say that proved the models wrong?
Yes you did say those things.. But I guess you forgot..
it was a provocative act directly aimed at getting the US into the middle east. That is why they waited through the Clinton years for a hawkish administration that would take the bait.
Right wing fantasy only. Or are you making excuses for the next republican president when he searches for and 'finds' excuses to start new mid east war so his buddies can buy new yachts.
No US wars started and we are enjoying the wisdom to leave stuff alone that can't be fixed economically.
Let me say this. I am done with this because you are wrong and so far from understanding that you don't even understand how wrong you are.
If you search google "math stackexchange expected travel of a random walk in arbitrary"
And read the first link.
""This is clearly a lot bigger than the expected value, which is 00. This makes sense, intuitively, if you draw out a normal distribution. Note that because you are adding random independent variables with a well-defined mean and variance it's OK to make the assumption of an approximate normal distribution, by the central limit theorem. The approximation gets better with NN. Now, values cancel out in this normal distribution, leaving a mean of 00, but distances don't.""
google "math stackexchange random walk"
""Suppose the walk approaches a constant aa as time goes to infinity. Suppose the walk is close to aa at some large time. Where will it be one time step later?""
Pretty much exactly what I told you with infinity plus one.