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However, it is (non-strictly) increasing, i.e. α ≤ β → α·γ ≤ β·γ. Multiplication of ordinals is not in general commutative. Specifically, a natural number greater than 1 never commutes with any infinite ordinal, and two infinite ordinals α and β commute if and only if α m = β n for some nonzero natural numbers m and n.
The comma operator separates expressions (which have value) in a way analogous to how the semicolon terminates statements, and sequences of expressions are enclosed in parentheses analogously to how sequences of statements are enclosed in braces: [1] (a, b, c) is a sequence of expressions, separated by commas, which evaluates to the last expression c, while {a; b; c;} is a sequence of ...
The sorting mode becomes numeric if the first 5 cells contain a number only (comma and period used in number formatting are accepted as number). The numeric sorting order is maintained even when text is found in the cells that follow the 5th cell. 123,564,589.7e12 is in scientific notation and is treated as a number. An empty cell is treated as ...
The comma is used in many contexts and languages, mainly to separate parts of a sentence such as clauses, and items in lists mainly when there are three or more items listed. The word comma comes from the Greek κόμμα (kómma), which originally meant a cut-off piece, specifically in grammar, a short clause. [1] [2]
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A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758 Extravagant numbers
[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. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of ...
"A comma goes before 'and' or 'or' in a series of three or more: Sn, K, Na, and Li lines are invisible." Plain English Handbook, Revised Edition (McCormick-Mathers Publishing Co., 1959), § 483, p. 78 "Use commas to separate the items in a series of words, phrases, or short clauses: The farmer sold corn, hay, oats, potatoes, and wheat."
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