In 1927 Felix Hausdorff wrote "The Equivalence Theorem can then be written in the suggestive form: If a≤b and a≥b, then a=b." At first sight this sentence seems eminently reasonable and clear. Surprisingly, though, this is nixed by the discovery that what Hausdorff meant by ≤ is not what we mean today! The issues involved led to decades of uncertainty, sometimes confusion, and evolution about cardinal numbers from Georg Cantor onward that can fascinate and motivate both us and our students today. Come to be challenged and find out all about it. And bring some paper and a writing implement.