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Halmos Tombstone
In mathematics, the tombstone, halmos, end-of-proof, or Q.E.D. symbol "∎" (or "□") is a symbol used to denote the end of a proof, in place of the traditional abbreviation "Q.E.D." for the Latin phrase "''quod erat demonstrandum''". It is inspired by the typographic practice of '' end marks'', an element that marks the end of an article. In Unicode, it is represented as character . Its graphic form varies, as it may be a hollow or filled rectangle or square. In AMS-LaTeX, the symbol is automatically appended at the end of a proof environment \begin ... \end. It can also be obtained from the commands \qedsymbol, \qedhere or \qed (the latter causes the symbol to be right aligned). It is sometimes called a "Halmos finality symbol" or "halmos" after the mathematician Paul Halmos, who first used it in a mathematical context in 1950. He got the idea of using it from seeing end marks in magazines, that is, typographic signs that indicate the end of an article. In his memoir ''I Wan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Halmos Symbols
Paul Richard Halmos ( hu, Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor. He has been described as one of The Martians. Early life and education Born in Hungary into a Jewish family, Halmos arrived in the U.S. at 13 years of age. He obtained his B.A. from the University of Illinois, majoring in mathematics, but fulfilling the requirements for both a math and philosophy degree. He took only three years to obtain the degree, and was only 19 when he graduated. He then began a Ph.D. in philosophy, still at the Champaign–Urbana campus; but, after failing his masters' oral exams, he shifted to mathematics, graduating in 1938. Joseph L. Doob supervised his dissertation, titled ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Typography
Typography is the art and technique of arranging type to make written language legible, readable and appealing when displayed. The arrangement of type involves selecting typefaces, point sizes, line lengths, line-spacing ( leading), and letter-spacing (tracking), as well as adjusting the space between pairs of letters (kerning). The term ''typography'' is also applied to the style, arrangement, and appearance of the letters, numbers, and symbols created by the process. Type design is a closely related craft, sometimes considered part of typography; most typographers do not design typefaces, and some type designers do not consider themselves typographers. Typography also may be used as an ornamental and decorative device, unrelated to the communication of information. Typography is the work of typesetters (also known as compositors), typographers, graphic designers, art directors, manga artists, comic book artists, and, now, anyone who arranges words, letters, numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
End Mark
End mark may refer to * Any terminal punctuation at the end of a sentence ** Especially the full stop (period) * A symbol, such as a bullet, tombstone or miniature logo, used primarily in magazine A magazine is a periodical publication, generally published on a regular schedule (often weekly or monthly), containing a variety of content. They are generally financed by advertising, purchase price, prepaid subscriptions, or by a combinatio ... writing, that indicates the end of an article (especially one that has been interrupted by advertising or by being split up across different sections of the publication for layout purposes). {{disambiguation Punctuation Typographical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expressed in most of the world's writing systems. The standard, which is maintained by the Unicode Consortium, defines as of the current version (15.0) 149,186 characters covering 161 modern and historic script (Unicode), scripts, as well as symbols, emoji (including in colors), and non-visual control and formatting codes. Unicode's success at unifying character sets has led to its widespread and predominant use in the internationalization and localization of computer software. The standard has been implemented in many recent technologies, including modern operating systems, XML, and most modern programming languages. The Unicode character repertoire is synchronized with Universal Coded Character Set, ISO/IEC 10646, each being code-for-code id ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AMS-LaTeX
AMS-LaTeX is a collection of LaTeX document classes and packages developed for the American Mathematical Society (AMS). Its additions to LaTeX include the typesetting of multi-line and other mathematical statements, document classes, and fonts containing numerous mathematical symbols. It has largely superseded the plain TeX macro package AMS-TeX. AMS-TeX was originally written by Michael Spivak, and was used by the AMS from 1983 to 1985. MathJax supports AMS-LaTeX through extensions. The following code of the LaTeX2e produces the AMS-LaTeX logo: %%% -- AMS-LaTeX_logo.tex ------- \documentclass \usepackage \begin \AmS-\LaTeX \end The package has a suite of facilities to format multi-line equations. For example, the following code, \begin y &= (x+1)^2 \\ &= x^2+2x+1 \end causes the equals signs in the two lines to be aligned with one another, like this: : \begin y &= (x+1)^2 \\ &= x^2+2x+1 \end AMS-LaTeX also includes many flexible c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Halmos
Paul Richard Halmos ( hu, Halmos Pál; March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor. He has been described as one of The Martians. Early life and education Born in Hungary into a Jewish family, Halmos arrived in the U.S. at 13 years of age. He obtained his B.A. from the University of Illinois, majoring in mathematics, but fulfilling the requirements for both a math and philosophy degree. He took only three years to obtain the degree, and was only 19 when he graduated. He then began a Ph.D. in philosophy, still at the Champaign–Urbana campus; but, after failing his masters' oral exams, he shifted to mathematics, graduating in 1938. Joseph L. Doob supervised his dissertation, titled ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magazine
A magazine is a periodical publication, generally published on a regular schedule (often weekly or monthly), containing a variety of content. They are generally financed by advertising, purchase price, prepaid subscriptions, or by a combination of the three. Definition In the technical sense a ''journal'' has continuous pagination throughout a volume. Thus '' Business Week'', which starts each issue anew with page one, is a magazine, but the '' Journal of Business Communication'', which continues the same sequence of pagination throughout the coterminous year, is a journal. Some professional or trade publications are also peer-reviewed, for example the '' Journal of Accountancy''. Non-peer-reviewed academic or professional publications are generally ''professional magazines''. That a publication calls itself a ''journal'' does not make it a journal in the technical sense; ''The Wall Street Journal'' is actually a newspaper. Etymology The word "magazine" derives from Arabic , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Typography
Typography is the art and technique of arranging type to make written language legible, readable and appealing when displayed. The arrangement of type involves selecting typefaces, point sizes, line lengths, line-spacing ( leading), and letter-spacing (tracking), as well as adjusting the space between pairs of letters (kerning). The term ''typography'' is also applied to the style, arrangement, and appearance of the letters, numbers, and symbols created by the process. Type design is a closely related craft, sometimes considered part of typography; most typographers do not design typefaces, and some type designers do not consider themselves typographers. Typography also may be used as an ornamental and decorative device, unrelated to the communication of information. Typography is the work of typesetters (also known as compositors), typographers, graphic designers, art directors, manga artists, comic book artists, and, now, anyone who arranges words, letters, numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
-30-
-30- has been traditionally used by journalists in North America to indicate the end of a story or article that is submitted for editing and typesetting. It is commonly employed when writing on deadline and sending bits of the story at a time, via telegraphy, teletype, electronic transmission, or paper copy, as a necessary way to indicate the end of the article. It is also found at the end of press releases. There are many theories as to how the usage came into being, and why it is found in North America but not in other Anglophone nations. One theory is that the journalistic employment of -30- originated from the number's use during the American Civil War era in the 92 Code of telegraphic shorthand, where it signified the end of a transmission and that it found further favor when it was included in the Phillips Code of abbreviations and short markings for common use that was developed by the Associated Press wire service. Telegraph operators familiar with numeric wire signals su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Elements
Block Elements is a Unicode block containing square block symbols of various fill and shading. Used along with block elements are box-drawing characters, shade characters, and terminal graphic characters. These can be used for filling regions of the screen and portraying drop shadows. Its block name in Unicode 1.0 was Blocks. Character table Font coverage Font sets like Code2000 and the DejaVu family—include coverage for each of the glyphs in the Block Elements range, Unifont also contains all the glyphs. Among the fonts in widespread use, full implementation is provided by Segoe UI Symbol. The glyphs in Block Elements each share the same character width in most supported fonts, allowing them to be used graphically in row and column arrangements. However, the block doesn't contain a space character of its own and ASCII space may or may not render at the same width as Block Elements glyphs, as those characters are intended to be used exclusively for monospaced fonts. Compac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
End-of-file
In computing, end-of-file (EOF) is a condition in a computer operating system where no more data can be read from a data source. The data source is usually called a file or stream. Details In the C standard library, the character reading functions such as getchar return a value equal to the symbolic value (macro) EOF to indicate that an end-of-file condition has occurred. The actual value of EOF is implementation-dependent and must be negative (but is commonly −1, such as in glibc). Block-reading functions return the number of bytes read, and if this is fewer than asked for, then the end of file was reached or an error occurred (checking of errno or dedicated function, such as ferror is required to determine which). EOF character Input from a terminal never really "ends" (unless the device is disconnected), but it is useful to enter more than one "file" into a terminal, so a key sequence is reserved to indicate end of input. In UNIX the translation of the keystroke to EOF is pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
