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For example, the phrase, "John, my best friend" uses the scheme known as apposition. Tropes (from Greek trepein, 'to turn') change the general meaning of words. An example of a trope is irony, which is the use of words to convey the opposite of their usual meaning ("For Brutus is an honorable man; / So are they all, all honorable men").
On the other hand, figurative use of language (a later offshoot being the term figure of speech [citation needed]) is the use of words or phrases with a meaning that does make literal sense but that encourages certain mental associations or reflects a certain type of truth, [7] perhaps a more artistically presented one.
Sibilance is used most successfully in stanzas one and five. The writer uses sibilance to imitate the sound and atmosphere she describes. In stanza one, she is imitating the "silent sign," and in stanza five she is trying to create a serene atmosphere that is "soft" and "sweetly spoke" by using the soft "s" sound repeatedly.
According to Florian Cajori in A History of Mathematical Notations, Johann Rahn used both the therefore and because signs to mean "therefore"; in the German edition of Teutsche Algebra (1659) the therefore sign was prevalent with the modern meaning, but in the 1668 English edition Rahn used the because sign more often to mean "therefore".
When defining a term, do not use the phrase "if and only if". For example, instead of A function f is even if and only if f(−x) = f(x) for all x; write A function f is even if f(−x) = f(x) for all x. If it is reasonable to do so, rephrase the sentence to avoid the use of the word "if" entirely. For example,
Some illusory visual proofs, such as the missing square puzzle, can be constructed in a way which appear to prove a supposed mathematical fact but only do so by neglecting tiny errors (for example, supposedly straight lines which actually bend slightly) which are unnoticeable until the entire picture is closely examined, with lengths and angles ...
A classic joke involving stereotypes is the "Dictionary of Definitions of Terms Commonly Used in Math Lectures". [20] Examples include "Trivial: If I have to show you how to do this, you're in the wrong class", "Similarly: At least one line of the proof of this case is the same as before" and "This proof is left as an exercise to the reader."
A proof by example is an argument whereby a statement is not proved but instead illustrated by an example. If done well, the specific example would easily generalize to a general proof. by inspection A rhetorical shortcut made by authors who invite the reader to verify, at a glance, the correctness of a proposed expression or deduction.