A pebble dropped in a pond creates ripples of concentric circles. Each larger circle having infinitely more points than the smaller ones inside. If we use any arbitrary size for the unit "point" with each point existing on the end of its own radius line and that the smallest circle contains all points and thus all radius lines from the epicenter, how do we account for the "extra" radius lines needed to create the next larger circle and so on in a spacial sense? Shouldn't there be gaps in the larger rings? Because there isn't gaps can this relate to the "creation of space from the big bang?
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The large circles have exactly the same number of points as the smaller circles, which in turn is the same as the number of points on the real line. All contain $\aleph_1$ points. See the Wikipedia article on aleph numbers for more.
Arguments based on comparing infinite (transfinite in this case) numbers are rather subtle and you should steer clear of them unless you've studied the area. In this case there is no obvious relationship to the Big Bang.
The Big Bang has a strict meaning as the zero time limit of the FLRW metric. However no physicist I know believes that the FLRW metric holds all the back to time zero because we all expect quantum gravity to modify the physics at very short times. So arguments about the creation of spacetime at the Big Bang are likely to be meaningless.
John Rennie
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