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A word equation is a formal equality:= = between a pair of words and , each over an alphabet comprising both constants (c.f. ) and unknowns (c.f. ). [1] An assignment h {\displaystyle h} of constant words to the unknowns of E {\displaystyle E} is said to solve E {\displaystyle E} if it maps both sides of E {\displaystyle E} to identical words.
Lewis Carroll's nyctographic alphabet. Each character had a large dot or circle in the upper-left corner. Beside the 26 letters of the alphabet, there were five additional characters for 'and', 'the', the corners of the letter 'f' to indicate that the following characters were digits ('figures'), the corners of the letter 'l' to indicate that they were letters, and the corners of the letter 'd ...
This counterintuitive result occurs because in the case where =, multiplying both sides by multiplies both sides by zero, and so necessarily produces a true equation just as in the first example. In general, whenever we multiply both sides of an equation by an expression involving variables, we introduce extraneous solutions wherever that ...
The unique pair of values a, b satisfying the first two equations is (a, b) = (1, 1); since these values also satisfy the third equation, there do in fact exist a, b such that a times the original first equation plus b times the original second equation equals the original third equation; we conclude that the third equation is linearly ...
Here thus in the history of equations the first letters of the alphabet became indicatively known as coefficients, while the last letters as unknown terms (an incerti ordinis). In algebraic geometry, again, a similar rule was to be observed: the last letters of the alphabet came to denote the variable or current coordinates.
In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous is often used for equations with some linear operator L on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homogeneous, as exemplified by ...
So we can write a = 2c, where c is also an integer. Substitution into the original equation yields 2b 2 = (2c) 2 = 4c 2. Dividing both sides by 2 yields b 2 = 2c 2. But then, by the same argument as before, 2 divides b 2, so b must be even. However, if a and b are both even, they have 2 as a common factor.
Many letters of the Latin alphabet, both capital and small, are used in mathematics, science, and engineering to denote by convention specific or abstracted constants, variables of a certain type, units, multipliers, or physical entities. Certain letters, when combined with special formatting, take on special meaning.