measure rainfall levels, and claiming that according to his thermometer the rainfall levels must be absurd.
             The alleged absurdity arising from removing books from an infinite library results from the misapplication of the finite 'subtraction' rules to an infinite collection, when subtraction is undefined for infinite numbers (Morriston 2002b, p. 152). In the Hilbert's Hotel example, the 'number' of infinite guests should not be determined as one would determine 'numbers' in a finite hotel (where adding one more guest to a full hotel would in fact result in a higher number of guests). Under infinite set theory, the fact that the 'number' of rooms remains infinite, even after the arrival of the additional guest, is explicable according to the transfinite principle that 'an infinite collection can be put into a one-to-one correspondence with proper subsets of itself' (from Cantor&ap
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