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A normal form for a group G with generating set S is a choice of one reduced word in S for each element of G. For example: For example: The words 1, i , j , ij are a normal form for the Klein four-group with S = { i , j } and 1 representing the empty word (the identity element for the group).
In English, verbification typically involves simple conversion of a non-verb to a verb. The verbs to verbify and to verb, the first by derivation with an affix and the second by zero derivation, are themselves products of verbification (see autological word), and, as might be guessed, the term to verb is often used more specifically, to refer only to verbification that does not involve a ...
In June, Formula One launched the We Race As One initiative to fight racism, global inequity and the impact of COVID-19. The initiative used a rainbow logo, with the colours of all ten Formula One teams, also with the #WeRaceAsOne hashtag, and featured prominent We Race As One branding on vehicles (including the safety car) and signage on track ...
A reference to a standard or choice-free presentation of some mathematical object (e.g., canonical map, canonical form, or canonical ordering). The same term can also be used more informally to refer to something "standard" or "classic". For example, one might say that Euclid's proof is the "canonical proof" of the infinitude of primes.
AC – Axiom of Choice, [1] or set of absolutely continuous functions. a.c. – absolutely continuous. acrd – inverse chord function. ad – adjoint representation (or adjoint action) of a Lie group. adj – adjugate of a matrix. a.e. – almost everywhere. AFSOC - Assume for the sake of contradiction; Ai – Airy function. AL – Action limit.
For real numbers, this formula is true if we substitute (arbitrarily) =, but is false if = It is the presence of a free variable, rather than the inconstant truth value, that is important; for example, even for complex numbers, where the formula is always true, it is still not considered a sentence.
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A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language. Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics.