incommutableness

Example:The principle of incommutableness is crucial in understanding why the order of factors in multiplication cannot be arbitrarily swapped.

Definition:a property in mathematics where the order of operations cannot be changed without altering the result (e.g., in multiplication, 2 * 3 ≠ 3 * 2)

Example:In Boolean algebra, the incommutableness of logical operations like AND and OR is fundamental to the design of computer circuits.

Definition:the inability to interchange the order of logical operands without changing the outcome of a logical operation

Example:In quantum mechanics, the incommutableness of operators representing observables like position and momentum is a cornerstone of the theory.

Definition:the inability to measure two observables simultaneously, where their measurement order affects the outcome, indicating that the order of operations is significant