 126  A := A for notational simplicity. A = 0 and so A =1. A = 0 and still A =1. A = 0 but A = 1 as yet. A = 0 but A = 1 nonetheless. A = 0 but then A =1. A = 0 has one and only one solution. A = 0; if not: A = 0. A = 0; if so, A2 = 0. A = 1 contradicts A = 0. A = 0 is contradicted by A = 1. A = 1 or A = 0 according as A2 = 1 or A2 = 0. A = A amounts to A2 = A2. A = A as is usual with equality. A = A in principle: A comes of B doing C. A = A unless otherwise stated. A = A unless the contrary is stated. A = A, which is what we need. A = A with probability one. A = A; so nothing is to be proved. A = A. Proof: Immediate. A = A. Proof: Obvious. A = A. Proof: Straightforward. 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. 126 |
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