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Apr 26, 2018 at 17:27 comment added Leandro M. "You cannot compare an abstract concept of 'e' to the 'x' and its behaviour towards minus infinite to something concrete as the time in the universe." Seems I can, because I just did!
Apr 25, 2018 at 15:54 comment added PDuarte I'm sorry to disagree, but it seems to me that a mathematical evidence does not, necessarily, prove a physical problem. You cannot compare an abstract concept of 'e' to the 'x' and its behaviour towards minus infinite to something concrete as the time in the universe. Infinity concept of mathematics is abstract and should not be understood as a feasible reality.
Feb 18, 2015 at 3:32 vote accept Doug Coburn
Feb 16, 2015 at 20:59 comment added Leandro M. Now given a function defined on the real line augmented by the points at $-\infty$ and $+\infty$, you get a function defined on the semicircle. But since the semicircle is finite, you get something that's a little more agreeable to the intuition.
Feb 16, 2015 at 20:56 comment added Leandro M. Perhaps the following idea will help. Instead of trying to think about the entire real line, imagine that you place a circle with radius 1 tangent to it at the origin. Now given a point on the real line, you can draw a line from it to the center of the circle. Note where the line crosses the circle: that gives a one to one correspondence between points on the line and points on the bottom semicircle, except for the two points on the "equator" which would correspond to minus and plus infinity respectively.
Feb 16, 2015 at 17:15 comment added Doug Coburn Excellent point. In order for a monotonically increasing function to not reach infinity, the rate of increase must approach 0 over an infinite amount of time. It is hard to wrap my head around actually standing at time = infinity. We aren't approaching infinity, we've already arrived there. Doesnt that mean the rate of entropy increase can't still be approaching 0, it must be 0.
Feb 16, 2015 at 6:03 history answered Leandro M. CC BY-SA 3.0