 Recall Galileo’s paradox of infinity, based on the collision of the part-whole intuition and the bijection intuition, and his conclusion that one cannot apply the relations of ‘less than’, ‘equality’, and ‘greater than’ to infinite collections. Modern mathematical orthodoxy, embodied in contemporary set theory, rejects Galileo’s conclusion. That orthodoxy is grounded in the bijection intuition, following Cantor rather than Euclid and Bolzano. When there is a bijection between two sets, we say that they have the same cardinality. The notion of cardinality does not respect the part-whole intuition. For example, the squares of natural numbers are a proper subset of the natural numbers, but they have the same cardinality since they can be put in one-to-one correspondence.