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.
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Famous quotes containing the words ambiguous and/or expressions:
“The whole of natural theology ... resolves itself into one simple, though somewhat ambiguous proposition, That the cause or causes of order in the universe probably bear some remote analogy to human intelligence.”
—David Hume (1711–1776)
“Many expressions in the New Testament come naturally to the lips of all Protestants, and it furnishes the most pregnant and practical texts. There is no harmless dreaming, no wise speculation in it, but everywhere a substratum of good sense. It never reflects, but it repents. There is no poetry in it, we may say, nothing regarded in the light of beauty merely, but moral truth is its object. All mortals are convicted by its conscience.”
—Henry David Thoreau (1817–1862)