Ambiguity - Pedagogic Use of Ambiguous Expressions

Pedagogic Use of Ambiguous Expressions

Ambiguity can be used as a pedagogical trick, to force students to reproduce the deduction by themselves. Some textbooks give the same name to the function and to its Fourier transform:

.

Rigorously speaking, such an expression requires that ; even if function is a self-Fourier function, the expression should be written as ; however, it is assumed that the shape of the function (and even its norm ) depend on the character used to denote its argument. If the Greek letter is used, it is assumed to be a Fourier transform of another function, The first function is assumed, if the expression in the argument contains more characters or, than characters, and the second function is assumed in the opposite case. Expressions like or contain symbols and in equal amounts; they are ambiguous and should be avoided in serious deduction.