165. Expressing set-size equality. Bulletin of Symbolic Logic.21 (2015) 239. (Coauthor: Gerald Rising) AC ► JOHN CORCORAN AND GERALD RISING, Expressing set-size equality. Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA E-mail: corcoran@buffalo.edu The set of points on a sphere is the set of points one radius from its center and it equals the set of points on any one of its radii, where 'equals' means "is in one-one correspondence with". Each angle of an equilateral triangle equals each of the other two but it isn't either of them. Many fields routinely distinguish identity and equality. Nothing is something else, but many things equal something else [this BULLETIN, vol. 19 (2013), pp. 255–256]. Identity and equality are routinely expressed by singular relational verbs-for identity: 'is', 'is the same [...] as', 'is identical to'; for equality: 'equals', 'is equal to'. Separation is clear: in fact 'equals' often connotes "not identical"-given availability of 'is'. Plural predicates such as 'are equal' [this BULLETIN, vol. 19 (2013), pp. 254–5] often express equality. Plural predicates can also express identity, but less smoothly: zee and zed are the same letter; zee and zed are one letter-the plurality of 'are' clashes with the singularity of its grammatical complement. Moreover, two-name conjunctions (as 'zee and zed') often connote that the names denote distinct entities. Clarity is sadly diminished when numbers or sets are discussed. We routinely read, e.g., that two plus three equals five, even in contexts emphasizing that two plus three actually is five. Moreover, despite agreement that two sets in one-one correspondence are equal [in size, or cardinality], authors often avoid writing that two such sets are equal-without qualification such as 'numerically' or 'in size': perhaps because 'equals' is often enough misleadingly used for 'is the same set as'. Avoiding the natural verb 'equals' requires artificial substitutes: 'equipollent' [Suppes], 'equinumerous' [Boolos], 'similar' [Dedekind], 'equivalent' [Tarski], 'can be put in one-one correspondence with' [Huntington], etc. We review established substitutes, their rationales, and reasons stated for avoiding 'equals'.