# If the Universe is infinite, why isn't it of infinite density?

If we make the assumption that the Universe is infinite, and has an infinite number of hydrogen atoms, then why is it not of infinite density - because, under Schrodinger's wave equation the probability of an electron being at any given point is non-zero and any non-zero number multiplied by infinity is itself infinity?

Is the answer (a) I have made some basic error in physics, (b) the Universe is provably not infinite because of this - effectively a version of Obler's Paradox or (c) the Pauli exclusion principle means that electrons just cannot be anywhere?

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Having infinite number of hydrogen atoms is not a direct consequence of an infinite Universe. You must revise your hypothesis. –  Py-ser Jul 2 at 11:35
Who said it was a "direct consequence"? –  adrianmcmenamin Jul 2 at 15:31
It seemed so from your question. Could you refer to the source which gave you these information? –  Py-ser Jul 3 at 3:36

Your assumption is not true. For example: if the probability density function of the atoms decreases quadratic exponentially (i.e. $e^{-r^2}$), then their sum will be finite even in an infinite universe.