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In current practice, the single 'word' "iff" is almost always read as the four words "if and only if". However, in the preface of General Topology , Kelley suggests that it should be read differently: "In some cases where mathematical content requires 'if and only if' and euphony demands something less I use Halmos' 'iff ' ".
In English conditional sentences, the antecedent (protasis) is a dependent clause, most commonly introduced by the complementizer if.Other complementizers may also be used, such as whenever, unless, provided (that), and as long as.
A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will be cancelled." They are so called because the impact of the sentence’s main clause is conditional on a subordinate clause.
The first published English grammar was a Pamphlet for Grammar of 1586, written by William Bullokar with the stated goal of demonstrating that English was just as rule-based as Latin. Bullokar's grammar was faithfully modeled on William Lily's Latin grammar, Rudimenta Grammatices (1534), used in English schools at that time, having been ...
The English modal auxiliary verbs are a subset of the English auxiliary verbs used mostly to express modality, properties such as possibility and obligation. [a] They can most easily be distinguished from other verbs by their defectiveness (they do not have participles or plain forms [b]) and by their lack of the ending ‑(e)s for the third-person singular.
In mathematics, theorems are often stated in the form "P is true if and only if Q is true". Because, as explained in previous section, necessity of one for the other is equivalent to sufficiency of the other for the first one, e.g. P ⇐ Q {\displaystyle P\Leftarrow Q} is equivalent to Q ⇒ P {\displaystyle Q\Rightarrow P} , if P is necessary ...