When a rubber band is stretched, or a battery is charged, or two massive objects are separated, the potential energy of all these systems increases in each situation. Now say that any of these systems were suspended in space. If we were to measure the gravitational field of the uncharged...
Thanks for your answer micromass. I was assuming the continuum hypothesis (CH) to be true when I made this post; I am familiar with thinking of |\Re| as equal to \aleph_1.
In the case that the CH is true, the example of the Stone-Cech compactification was the sort of thing I was looking for...
If we accept that there does indeed exist a set whose cardinality is between \aleph_0 and \aleph_1, what would such a set look like?
I know that in ZM-C we can choose to either add the continuum hypotheses or not, but if we chose to negate it, that means that there definitely is a set greater...
I know that we can easily construct a set whose cardinality is strictly greater than that of the set of real numbers by taking P(\Re) where P denotes the power-set operator. But as far as I am aware there aren't really any uses for this class of sets (up to bijection), or any intuitive ways of...