Mathematics of Eternity Prove The Universe Must Have Had A Beginning -- Part II: "To make the point simply, imagine Hilbertville, a one-dimensional semi-infinite city, whose border is at x = 0: The population is infinite and uniformly fills the positive axis x > 0: Each citizen has an identical telescope with a finite power. Each wants to know if there is a boundary to the city. It is obvious that only a finite number of citizens can see the boundary at x = 0. For the infinite majority the city might just as well extend to the infinite negative axis...
Thus, assuming he is typical, a citizen who has not yet studied the situation should bet with great confidence that he cannot detect a boundary. This conclusion is independent of the power of the telescopes as long as it is finite..."
He finishes with this: "We may conclude that there is a beginning, but in any kind of inflating cosmology the odds strongly (infinitely) favor the beginning to be so far in the past that it is eff ectively at minus infinity."
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