- #1

Hornbein

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Let's suppose that the universe is infinite and the size of galaxies is normally distributed. Then there is no largest galaxy. Conclusion : the size is not normally distributed.

The same is true for any distribution that has a positive probability for all possibilities. So that can't be the case. All that is left is some distribution that has a maximum possible size. In this case there will still be no largest galaxy. Instead there will be galaxies approaching this limit in size but never reaching it. No matter how close a galaxy comes to the limit there will always be a infinitesimally larger galaxy.

Or is this true? In an infinite universe there could be a great many galaxies of probability zero that are larger than the limit. But the chance that Earthlings would ever observe such a galaxy is also zero so it is of no practical interest. Then again it is possible that there truly is a hard limit and a galaxy with diameter greater than X is impossible. But as noted before, that doesn't mean that there is a galaxy of maximum size.

The same is true for any distribution that has a positive probability for all possibilities. So that can't be the case. All that is left is some distribution that has a maximum possible size. In this case there will still be no largest galaxy. Instead there will be galaxies approaching this limit in size but never reaching it. No matter how close a galaxy comes to the limit there will always be a infinitesimally larger galaxy.

Or is this true? In an infinite universe there could be a great many galaxies of probability zero that are larger than the limit. But the chance that Earthlings would ever observe such a galaxy is also zero so it is of no practical interest. Then again it is possible that there truly is a hard limit and a galaxy with diameter greater than X is impossible. But as noted before, that doesn't mean that there is a galaxy of maximum size.

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