Concepts of Modern Mathematics

Published: June 14, 2024

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This means, for example, that from the facts that 1 ≡ 8 and 3 ≡ 10 (mod 7) we can deduce that 1+3 = 4 is congruent to 8+10 = 18; and that 1×3 = 3 is congruent to 8×10 = 80. As a check, the differences 14 and 77 are both divisible by 7. (Location 657)
10 Boolean algebra is of some use in the design of logic circuits for computers (see e.g. Rutherford, Introduction to Lattice Theory, Oliver & Boyd, 1965, pp. 31—40, 58-74). Apart from its connection with set theory it has little relevance to the main body of mathematics. However, quite a deep theory exists. See P. R. Halmos, Lectures on Boolean Algebras, Van Nostrand, 1963. (Location 5542)

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This means, for example, that from the facts that 1 ≡ 8 and 3 ≡ 10 (mod 7) we can deduce that 1+3 = 4 is congruent to 8+10 = 18; and that 1×3 = 3 is congruent to 8×10 = 80. As a check, the differences 14 and 77 are both divisible by 7. (Location 657)
10 Boolean algebra is of some use in the design of logic circuits for computers (see e.g. Rutherford, Introduction to Lattice Theory, Oliver & Boyd, 1965, pp. 31—40, 58-74). Apart from its connection with set theory it has little relevance to the main body of mathematics. However, quite a deep theory exists. See P. R. Halmos, Lectures on Boolean Algebras, Van Nostrand, 1963. (Location 5542)