what do the 3 dots mean in math
therefore sign the therefore sign
title: Therefore sign text: Therefore sign In logical argument and mathematical proof, the therefore sign (∴) is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read "therefore". It is encoded at . For common use in Microsoft Office hold the ALT key and type "8756". While it is not generally used in formal writing, it is used in mathematics and shorthand. It is complementary to . According to Cajori, "A History of Mathematical Notations," Johann Rahn used both the "therefore" and "because" signs to mean "therefore"; title: Multiplication text: referring to a group via the indication of the set and operation, the dot is used, e.g., our first example could be indicated by formula_32 Numbers can "count" (3 apples), "order" (the 3rd apple), or "measure" (3.5 feet high); as the history of mathematics has progressed from counting on our fingers to modelling quantum mechanics, multiplication has been generalized to more complicated and abstract types of numbers, and to things that are not numbers (such as matrices) or do not look much like numbers (such as quaternions). When multiplication is repeated, the resulting operation is known as exponentiation. For instance, title: Principia Mathematica text: of parentheses. This uses the definition (followed by the explanatory comment): Example 2, with double, triple, and quadruple dots: stands for Example 3, with a double dot indicating a logical symbol (from volume 1, page 10): stands for where the double dot represents the logical symbol ∧, and its right operand consists of everything after it because it has priority over the single dots. Later in section ✸14, brackets "[ ]" appear, and in sections ✸20 and following, braces "{ }" appear. Whether these symbols have specific meanings or are just for visual clarification is unclear. Unfortunately the single dot title: Polygonal number text: Polygonal number In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots are thought of as alphas (units). These are one type of 2-dimensional figurate numbers. The number 10 for example, can be arranged as a triangle (see triangular number): But 10 cannot be arranged as a square. The number 9, on the other hand, can be (see square number): Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number): By convention, 1 is the first polygonal number title: Therefore sign text: specialized keyboards and fonts, and to prevent compatibility issues, it's often substituted by a colon followed by a period (":.") even if it's considered more elegant to use the original therefore character in printing. Therefore sign In logical argument and mathematical proof, the therefore sign (∴) is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read "therefore". It is encoded at . For common use in Microsoft Office hold the ALT key and type "8756". While it is not generally used in