Associative thoughts are things that you think of because you see, hear, or think of something that reminds you of those things or which you associate with those things. The associative guilt was ingrained in his soul. reminding you of something else
1 In abstract algebra, a dyadic operation in which two sequential operations on three arguments can first operate on either the first two or the last two arguments, producing the same result in either case: (a + b) + c = a + (b + c) 2 In algebra, the associative law for addition and multiplication The algebraic law for evaluating the result of grouping terms or factors in different ways, as in conventional arithmetic: a + (b + c) = (a + b) + c a * (b * c) = (a * b) * c Also see: commutative and distributive
A dyadic operation in which two sequential operations on three arguments can first operate on either the first two or the last two arguments, producing the same result in either case: (a + b) + c = a + (b + c) Also see: commutative and distributive
in mathematics, law holding that for a given operation combining three quantities, two at a time, the initial pairing is arbitrary; e.g., using the operation of addition, the numbers 2, 3, and 4 may be combined (2+3)+4=5+4=9 or 2+(3+4)=2+7=9. More generally, in addition, for any three numbers a, b, and c the associative law is expressed as (a+b)+c=a+(b+c). Multiplication of numbers is also associative, i.e., (a×b)×c=a×(b×c). In general, any binary operation, symbolized by [symbol], joining mathematical entities A, B, and C obeys the associative law if (A[symbol]B)[symbol]C=A[symbol](B[symbol]C) for all possible choices of A, B, and C. Not all operations are associative. For example, ordinary division is not, since (60÷12)÷3=5÷3=5/3, while 60÷(12÷3)=60÷4=15. When an operation is associative, the parentheses indicating which quantities are first to be combined may be omitted, e.g., (2+3)+4=2+(3+4)=2+3+4
Two closely related laws of number operations. In symbols, they are stated: a + (b + c) = (a + b) + c, and a(bc) = (ab)c. Stated in words: The terms or factors may be associated in any way desired and the result will be the same. This holds for the numbers generally encountered: positive and negative, integral and fractional, rational and irrational, real and imaginary. Exceptions occur (e.g., in nonassociative algebras and divergent infinite series)
Two closely related laws of number operations. In symbols, they are stated: a + (b + c) = (a + b) + c, and a(bc) = (ab)c. Stated in words: The terms or factors may be associated in any way desired and the result will be the same. This holds for the numbers generally encountered: positive and negative, integral and fractional, rational and irrational, real and imaginary. Exceptions occur (e.g., in nonassociative algebras and divergent infinite series). See also commutative law, distributive law
A type of learning principle based on the assumption that ideas and experiences reinforce one another and can be linked to enhance the learning process
Determines whether you do the left operator first or the right operator first, when you have "A operator B operator C", if the two operators are of the same precedence Operators like + are left associative, while operators like ** are right associative See the section "Operators" in Chapter 2, The Gory Details, for a list of associativity
The associativity of a binary operator determines the order in which several of them in a row are done If the operator is left-associative (or, equivalently, if it associates to the left) then that operator is applied from left to right If it is right-associative (or, equivalently, it associates to the right) then that operator is applied from right to left For example, - is left-associative So 10 - 4 - 3 is computed from left to right First, 10 - 4 is computed, yielding 6 Then 6 - 3 is computed, yielding 3 If you insert parentheses to force this, you get (10 - 4) - 3 As you can see, the parentheses are toward the left On the other hand, ^ is right associative (^ is exponentiation) So 3^3^2 yields the same result as 3^9, not as 27^2 See E7
Determines whether you do the left operator first or the right operator first when you have "A operator B operator C" and the two operators are of the same precedence Operators like + are left associative, while operators like ** are right associative See Chapter 3, "Unary and Binary Operators", for a list of operators and their associativity