The Hardest Logic Puzzle Ever is a logic puzzle so called by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996. Boolos' article includes multiple ways of solving the problem. A translation in Italian was published earlier in the newspaper La Repubblica, under the title L'indovinello più difficile del mondo.
It is stated as follows:
Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter...
Fatalism is a philosophical doctrine that stresses the subjugation of all events or actions to fate.
Fatalism generally refers to any of the following ideas:
The view that we are powerless to do anything other than what we actually do. Included in this is that humans have no power to influence the future, or indeed, their own actions. This belief is very similar to predeterminism.
An attitude of resignation in the face of some future event or events which are thought to be inevitable. Friedrich Nietzsche named this idea "Turkish fatalism" in his book The Wanderer and His Shadow.
That acceptance...
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I need to show that the function $f(x) = \frac{1}{1-x}$ is equal to its Taylor Series (about $a=0$) on $(-1,1)$.
Thus far, I have found the Taylor Series: $\frac{1}{1-x} \approx \sum_{k=0}^{\infty}x^{k}$, and since $f^{(n+1)}(x) = \frac{(n+1)!}{(1-x)^{n+2}}$, the Lagrange Error Formula gives us ...
