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A = A. Proof: Trivial. A = A . On the contrary, A = {A}. A • 12 contains A • 2, A • 3, A • 4 and A • 6. A U {A} consists of A and the elements of A. A U {A} contains A. A e {A} irrespective of whether or not B e {A}. A e {A}. Reason: B e {A} ^ B = A. A e {A}. For, B e {A} implies B = A. A < A with equality holding iff A = A. A = B is the condition that A be B. A < B < C, the second inequality following from (1.1). A =1 but A, however, vanishes. A = A. Counterexample: 1 = 1. A = 0, but it may fail in general. A ^ A, A e B, is the identity indexing of B. A ^ B. The converse is the reverse implication B ^ A. A2 divides by A. —B holds, for —A. {A} is obviously nonempty; in symbols, {A} = 0. {A} is prepared to become A. {A} prompts A being a set. {A} = {A} is plain and immediate from A = A. {A} = {{A}} abuses the language. {A} = {{A}} is a notational juggling. {A} \ A is disjoint from A. i before e except after c, or when sounded like “ay” as in “neighbor” or “weigh.” |A| is termed the modulus of A. A necessary and sufficient condition that A2 be 0 is that A be 0. Absence is a state; lack implies shortage. Acquire fluent knowledge of English. Active ed-participles are rarely used in premodification (exception: adverbially modified). Acute: e. Ad (1.1): Apply Theorem 2.1. Adduce reasons and examples. Adhere to principle. Adherent points produce a closure. Adjective phrases with 127
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