As $k$ approaches infinity, so does the common from the $k$ payouts. Powering this boundless development is The point that everytime an not likely consequence happens, the payout is so substantial that, when averaged With all the payout of a lot more probably results, the average is skewed up.

$begingroup$ As drhab mentioned in his reply, your instinct tells you that $infty instances 2$ needs to be $infty$. But that instinct is determined by That which you understood

$begingroup$ Infinite simply signifies "not finite", equally during the colloquial sense and in the technological sense (in which we very first outline the time period "finite"). There is absolutely no technological definition that i'm aware about for "transfinite".

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Lets Do this without Taylor series. A perform that can be expressed by a real energy collection known as real analytic. All that is necessary is that every one derivatives are bigger than or equal to $0$. Obviously this holds for $e^x$.

How can fighter jets compensate to the curvature of your earth whenever they're traveling so very low to the ground?

$begingroup$ Within the problem alone, arises the fact that you are thinking about it at an intuitive way. The answer to the intuitive query "is 2x = x?" then is YES. But see that x is surely an "infinite range", and so, saying that two instances infinite is infinite isn't a major deal.

 

– user14972 Commented Jan 25, 2014 at 12:forty eight $begingroup$ Not likely.. I remaining it to your reader no matter whether he hopes to suppose that, or just evaluate the definition to generally be a description of what is infinite. Indeed there may be a lot of things that "have larger magnitude than any finite amount", and double any these kinds of point also satisfies precisely the same residence.

 

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As for your personal question about no matter whether a functionality can be expressed being a series or not, to answer it I feel you'll want to say something about calculus. What I imply is if a "good" functionality $file(x)$ includes a series illustration at a degree $a$ then the sequence is presented by