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Blackboard Bold
Blackboard bold is a typeface style that is often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical or near-vertical lines) are doubled. The symbols usually denote number sets. One way of producing blackboard bold is to double-strike a character with a small offset on a typewriter. Thus, they are also referred to as double struck. In typography, such a font with characters that are not solid is called an "inline", "shaded", or "tooled" font. History Origin In some texts, these symbols are simply shown in bold type. Blackboard bold in fact originated from the attempt to write bold letters on blackboards in a way that clearly differentiated them from non-bold letters (by using the edge rather than the point of a chalk). It then made its way back into print form as a separate style from ordinary bold, possibly starting with the original 1965 edition of Gunning and Rossi's textbook on complex analysis. Use in textbooks In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blackboard Bold
Blackboard bold is a typeface style that is often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical or near-vertical lines) are doubled. The symbols usually denote number sets. One way of producing blackboard bold is to double-strike a character with a small offset on a typewriter. Thus, they are also referred to as double struck. In typography, such a font with characters that are not solid is called an "inline", "shaded", or "tooled" font. History Origin In some texts, these symbols are simply shown in bold type. Blackboard bold in fact originated from the attempt to write bold letters on blackboards in a way that clearly differentiated them from non-bold letters (by using the edge rather than the point of a chalk). It then made its way back into print form as a separate style from ordinary bold, possibly starting with the original 1965 edition of Gunning and Rossi's textbook on complex analysis. Use in textbooks In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chicago Manual Of Style
(''City in a Garden''); I Will , image_map = , map_caption = Interactive Map of Chicago , coordinates = , coordinates_footnotes = , subdivision_type = Country , subdivision_name = United States , subdivision_type1 = State , subdivision_type2 = Counties , subdivision_name1 = Illinois , subdivision_name2 = Cook and DuPage , established_title = Settled , established_date = , established_title2 = Incorporated (city) , established_date2 = , founder = Jean Baptiste Point du Sable , government_type = Mayor–council , governing_body = Chicago City Council , leader_title = Mayor , leader_name = Lori Lightfoot ( D) , leader_title1 = City Clerk , leader_name1 = Anna Valencia ( D) , unit_pref = Imperial , area_footnotes = , area_tot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ball (mathematics)
In mathematics, a ball is the solid figure bounded by a ''sphere''; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them). These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. A ''ball'' in dimensions is called a hyperball or -ball and is bounded by a ''hypersphere'' or ()-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a line segment. In other contexts, such as in Euclidean geometry and informal use, ''sphere'' is sometimes used to mean ''ball''. In the field of topology the closed n-dimensional ball is often denoted as B^n or D^n while the open n-dimensional ball is \operatorname B^n or \o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Integer
In algebraic number theory, an algebraic integer is a complex number which is integral over the integers. That is, an algebraic integer is a complex root of some monic polynomial (a polynomial whose leading coefficient is 1) whose coefficients are integers. The set of all algebraic integers is closed under addition, subtraction and multiplication and therefore is a commutative subring of the complex numbers. The ring of integers of a number field , denoted by , is the intersection of and : it can also be characterised as the maximal order of the field . Each algebraic integer belongs to the ring of integers of some number field. A number is an algebraic integer if and only if the ring \mathbbalpha/math> is finitely generated as an abelian group, which is to say, as a \mathbb-module. Definitions The following are equivalent definitions of an algebraic integer. Let be a number field (i.e., a finite extension of \mathbb, the field of rational numbers), in other words, K = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Closure
In mathematics, particularly abstract algebra, an algebraic closure of a field ''K'' is an algebraic extension of ''K'' that is algebraically closed. It is one of many closures in mathematics. Using Zorn's lemmaMcCarthy (1991) p.21Kaplansky (1972) pp.74-76 or the weaker ultrafilter lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field ''K'' is unique up to an isomorphism that fixes every member of ''K''. Because of this essential uniqueness, we often speak of ''the'' algebraic closure of ''K'', rather than ''an'' algebraic closure of ''K''. The algebraic closure of a field ''K'' can be thought of as the largest algebraic extension of ''K''. To see this, note that if ''L'' is any algebraic extension of ''K'', then the algebraic closure of ''L'' is also an algebraic closure of ''K'', and so ''L'' is contained within the algebraic closure of ''K''. The algebraic closure of ''K'' is also the smallest algebraically closed fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Number
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (1 + \sqrt)/2, is an algebraic number, because it is a root of the polynomial . That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number 1 + i is algebraic because it is a root of . All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as and , are called transcendental numbers. The set of algebraic numbers is countably infinite and has measure zero in the Lebesgue measure as a subset of the uncountable complex numbers. In that sense, almost all complex numbers are transcendental. Examples * All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer and a (non-zero) natural number , satisfies the above definition, bec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adele Ring
Adele Laurie Blue Adkins (, ; born 5 May 1988), professionally known by the mononym Adele, is an English singer and songwriter. After graduating in arts from the BRIT School in 2006, Adele signed a record deal with XL Recordings. Her debut album, '' 19'', was released in 2008 and spawned the UK top-five singles " Chasing Pavements" and "Make You Feel My Love". The album was certified 8× platinum in the UK and triple platinum in the US. Adele was honoured with the Brit Award for Rising Star as well as the Grammy Award for Best New Artist. Adele released her second studio album, '' 21'', in 2011. It became the world's best-selling album of the 21st century, with sales of over 31 million copies. It was certified 18× platinum in the UK (the highest by a solo artist of all time) and Diamond in the US. According to ''Billboard'', ''21'' is the top-performing album in the US chart history, topping the ''Billboard'' 200 for 24 weeks (t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affine Space
In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments. In an affine space, there is no distinguished point that serves as an origin. Hence, no vector has a fixed origin and no vector can be uniquely associated to a point. In an affine space, there are instead '' displacement vectors'', also called ''translation'' vectors or simply ''translations'', between two points of the space. Thus it makes sense to subtract two points of the space, giving a translation vector, but it does not make sense to add two points of the space. Likewise, it makes sense to add a displacement vector to a point of an affine space, resulting in a new point translated from the starting point by that vector. Any vector space may be viewed as an affine spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LaTeX Logo
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms). It is a complex emulsion that coagulates on exposure to air, consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums. It is usually exuded after tissue injury. In most plants, latex is white, but some have yellow, orange, or scarlet latex. Since the 17th century, latex has been used as a term for the fluid substance in plants, deriving from the Latin word for "liquid". It serves mainly as defense against herbivorous insects. Latex is not to be confused with plant sap; it is a distinct substance, separately produced, and with different functions. The word latex is also used to refer to natural latex rubber, particularly non- vulcanized rubber. Such is the case in products like latex gloves, latex condoms and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LaTeX
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms). It is a complex emulsion that coagulates on exposure to air, consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums. It is usually exuded after tissue injury. In most plants, latex is white, but some have yellow, orange, or scarlet latex. Since the 17th century, latex has been used as a term for the fluid substance in plants, deriving from the Latin word for "liquid". It serves mainly as defense against herbivorous insects. Latex is not to be confused with plant sap; it is a distinct substance, separately produced, and with different functions. The word latex is also used to refer to natural latex rubber, particularly non- vulcanized rubber. Such is the case in products like latex gloves, latex con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Alphanumeric Symbols
Mathematical Alphanumeric Symbols is a Unicode block comprising styled forms of Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The letters in various fonts often have specific, fixed meanings in particular areas of mathematics. By providing uniformity over numerous mathematical articles and books, these conventions help to read mathematical formulas. Unicode now includes many such symbols (in the range U+1D400–U+1D7FF). The rationale behind this is that it enables design and usage of special mathematical characters (fonts) that include all necessary properties to differentiate from other alphanumerics, e.g. in mathematics an ''italic'' "𝐴" can have a different meaning from a ''roman'' letter "A". Unicode originally included a limited set of such letter forms in its Letterlike Symbols block before completing the set of Latin and Greek letter forms in this block beginning in version ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Letterlike Symbols
Letterlike Symbols is a Unicode block containing 80 characters which are constructed mainly from the glyphs of one or more letters. In addition to this block, Unicode includes full styled mathematical alphabets, although Unicode does not explicitly categorise these characters as being "letterlike". Symbols Glyph variants Variation selectors may be used to specify chancery (U+FE00) vs roundhand (U+FE01) forms, if the font supports them: The remainder of the set is at Mathematical Alphanumeric Symbols. Block Emoji The Letterlike Symbols block contains two emoji: U+2122 and U+2139. The block has four standardized variants defined to specify emoji-style (U+FE0F VS16) or text presentation (U+FE0E VS15) for the two emoji, both of which default to a text presentation. History The following Unicode-related documents record the purpose and process of defining specific characters in the Letterlike Symbols block: See also * Greek in Unicode * Latin script in Unicod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
