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The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
[2] In a sense, subtraction is the inverse of addition. That is, c = a − b if and only if c + b = a. In words: the difference of two numbers is the number that gives the first one when added to the second one. Subtraction follows several important patterns. It is anticommutative, meaning that
The history of money is the development over time of systems for the exchange of goods and services. Money is a means of fulfilling these functions indirectly and in general rather than directly, as with barter. Money may take a physical form as in coins and notes, or may exist as a written or electronic account.
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