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For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [ 2 ] [ 3 ] Thus, in the expression 1 + 2 × 3 , the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7 , and not (1 + 2) × 3 = 9 .
Alternative algebras are so named because they are the algebras for which the associator is alternating.The associator is a trilinear map given by [,,] = ().By definition, a multilinear map is alternating if it vanishes whenever two of its arguments are equal.
There are two basic types of outliners: one-pane or intrinsic, and two-pane or extrinsic, each with its strengths and weaknesses.. A one-pane outliner is known as an intrinsic outliner because the text itself is organized into an outline format—individual sections (such as paragraphs) of text can be collapsed or expanded, while keeping others in view.
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.
A style guide, or style manual, is a set of standards for the writing and design of documents, either for general use or for a specific publication, organization or field. The implementation of a style guide provides uniformity in style and formatting within a document and across multiple documents.
For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power. The word "raised" is usually omitted, and sometimes "power" as well, so 3 5 can be simply read "3 to the 5th", or "3 to the 5".
For example, the third triangular number is (3 × 2 =) 6, the seventh is (7 × 4 =) 28, the 31st is (31 × 16 =) 496, and the 127th is (127 × 64 =) 8128. The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7.
Each correct answer moves the contestant up a payout ladder (the question value determines the difficulty, regardless of grade level), and by completing the first set of ten questions, the contestant is offered a final, bonus question worth the grand prize from the highest primary school grade level (for example, fifth grade in the American ...