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From Wikipedia

Symbol

A symbol is something such as an object, picture, written word, sound, or particular mark that represents something else by association, resemblance, or convention. For example, a red octagon may be a symbol for "STOP". On maps, crossed sabres may indicate a battlefield. Numerals are symbols for numbers (amounts). All language consists of symbols. Personal names are symbols representing individuals.

Psychoanalysis and archetypes

Swiss psychoanalyst Carl Jung, who studied archetypes, proposed an alternative definition of symbol, distinguishing it from the term sign. In Jung's view, a sign stands for something known, as a word stands for its referent. He contrasted this with symbol, which he used to stand for something that is unknown and that cannot be made clear or precise. An example of a symbol in this sense isChrist as a symbol of the archetype called self. For example, written languages are composed of a variety of different symbols that create words. Through these written words, humans communicate with each other.Kenneth Burke described Homo sapiensas a "symbol-using, symbol making, and symbol misusing animal" to indicate that a person creates symbols in her or his life as well as misuses them. One example he uses to indicate his meaning behind symbol misuse is the story of a man who, when told a particular food item was whale blubber, could barely keep from throwing it up. Later, his friend discovered it was actually just a dumpling. But the man's reaction was a direct consequence of the symbol of "blubber" representing something inedible in his mind. In addition, the symbol of "blubber" for the man was created by him through various kinds of learning. Burke emphasizes that humans gain this type of learning that helps us create symbols by seeing various print sources, our life experiences, and symbols about the past.

Burke also goes on to describe symbols as also being derived from Sigmund Freud's work on condensation and displacement further stating that they are not just relevant to the theory of dreams, but also to "normal symbol systems". He says they are related through "substitution" where one word, phrase, or symbol is substituted for another in order to change the meaning. In other words, if a person does not understand a certain word or phrase, another person may substitute a synonym or symbol in order to get the meaning of the original word or phrase across. However, when faced with that new way of interpreting a specific symbol, a person may change their already formed ideas to incorporate the new information based on how the symbol is expressed to the person.

Etymology

The word symbol came to the English language by way of Middle English, from Old French, from Latin, from the Greekσ�μβολον (sýmbolon) from the root words συν- (syn-), meaning "together," and βολή (bolē), "a throw", having the approximate meaning of "to throw together", literally a "co-incidence", also "sign, ticket, or contract". The earliest attestation of the term is in the Homeric Hymn to Hermes where Hermes on seeing the tortoise exclaims σ�μβολον ἤδη μοι μέγ᾽ ὀνήσιμον "symbolon [symbol/sign/portent/encounter/chance find?] of joy to me!" before turning it into a lyre.

Role of context in symbolism

A symbol's meaning may be modified by various factors including popular usage, history, and contextual intent.

Historical meaning

This history of a symbol is one of many factors in determining a particular symbol's apparent meaning. Old symbols become reinterpreted, due perhaps to environmental changes. Consequently, symbols with emotive power carry problems analogous to false etymologies.

For example, the Rebel Flag of the American South predates the American Civil War. An early variant of the crossed bars resembled the Scottish Flag.

Juxtaposition

Juxtaposition further complicates the matter. Similar five–pointed stars might signify a law enforcement officer or a member of the armed services, depending the uniform.


Power symbol

A power symbol is a symbol indicating that a control activates or deactivates a particular device. It incorporates line and circle figures, with the arrangement informed by the function of the control. The universal power symbols are described in the International Electrotechnical Commission 60417 standard, Graphical symbols for use on equipment, appearing in the 1973 edition of the document (as IEC 417) and informally used earlier.

Definitions

Standby symbol ambiguity

Because the exact meaning of the standby symbol on a given device may be unclear until the control is tried, it has been proposed that a separate sleep symbol, a crescent moon, instead be used to indicate a low power state. Proponents include the California Energy Commission and the Institute of Electrical and Electronics Engineers. Under this proposal, the older standby symbol would be redefined as a generic "power" indication, in cases where the difference between it and the other power symbols would not present a safety concern. This alternative symbology was published as IEEE standard 1621 on 2004-12-08.

In popular culture

The standby symbol, frequently seen on personal computers, is a popular icon among technology enthusiasts. It can even be found on T-shirts. It has also been used in corporate logos, such as for Gateway, Inc. (circa 2002), Staples, Inc. easytech, Exelon and others, and even as personal tattoos. In March 2010, the New York City health department announced they would be using it on condom wrappers.


Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics. Mathematical notations include relatively simple symbolic representations, such as numbers 1 and 2, function symbols sin and +; conceptual symbols, such as lim, dy/dx, equations and variables; and complex diagrammatic notations such as Penrose graphical notation and Coxeter-Dynkin diagrams.

Definition

A mathematical notation is a writing system used for recording concepts in mathematics.

  • The notation uses symbols or symbolic expressions which are intended to have a precise semantic meaning.
  • In the history of mathematics, these symbols have denoted numbers, shapes, patterns, and change. The notation can also include symbols for parts of the conventional discourse between mathematicians, when viewing mathematics as a language.

The media used for writing are recounted below, but common materials currently include paper and pencil, board and chalk (or dry-erase marker), and electronic media. Systematic adherence to mathematical concepts is a fundamental concept of mathematical notation. (See also some related concepts: Logical argument, Mathematical logic, and Model theory.)

Expressions

A mathematical expression is a sequence of symbols which can be evaluated. For example, if the symbols represent numbers, the expressions are evaluated according to a conventional order of operations which provides for calculation, if possible, of any expressions within parentheses, followed by any exponents and roots, then multiplications and divisions and finally any additions or subtractions, all done from left to right. In a computer language, these rules are implemented by the compilers. For more on expression evaluation, see the computer science topics: eager evaluation, lazy evaluation, and evaluation operator.

Precise semantic meaning

Modern mathematics needs to be precise, because ambiguous notations do not allow formal proofs. Suppose that we have statements, denoted by some formal sequence of symbols, about some objects (for example, numbers, shapes, patterns). Until the statements can be shown to be valid, their meaning is not yet resolved. While reasoning, we might let the symbols refer to those denoted objects, perhaps in a model. The semantics of that object has a heuristic side and a deductive side. In either case, we might want to know the properties of that object, which we might then list in an intensional definition.

Those properties might then be expressed by some well-known and agreed-upon symbols from a table of mathematical symbols. This mathematical notation might include annotation such as

  • "All x", "No x", "There is an x" (or its equivalent, "Some x"), "A set", "A function"
  • "A mapping from the real numbers to the complex numbers"

In different contexts, the same symbol or notation can be used to represent different concepts. Therefore, to fully understand a piece of mathematical writing, it is important to first check the definitions that an author gives for the notations that are being used. This may be problematic if the author assumes the reader is already familiar with the notation in use.

History

Counting

It is believed that a mathematical notation to represent counting was first developed at least 50,000 years ago — early mathematical ideas such as finger counting have also been represented by collections of rocks, sticks, bone, clay, stone, wood carvings, and knotted ropes. The tally stick is a timeless way of counting. Perhaps the oldest known mathematical texts are those of ancient Sumer. The Census Quipu of the Andes and the Ishango Bone from Africa both used the tally mark method of accounting for numerical concepts.

The development of zero as a number is one of the most important developments in early mathematics. It was used as a placeholder by the Babylonians and Greek Egyptians, and then as an integer by the Mayans, Indians and Arabs. (See From Yahoo Answers

Question:I can't really find this definition anywhere.I know < is less than, and > is greater than, but << and >> seem to work different. I'm working on a math problem, and it wants me to prove that (ln(x))^2 << sqrt(x) But I've no idea what it's actually asking. I thought it meant something like, it is always lesser than, or is always greater than, but ln(x)^2 is not always lesser than the sqrt(x), is it? Like, when x = 20, that's not true.

Answers:Much greater and much less than.

Question:In math or Algebra what so these symbols mean? * , / , and ^ I think the Astrix is multiply and the forward slash is divide. What about the others?

Answers:Hi: * mean multiplication / means divide ^ mean take the power of ( or how many time a number is multiplied by itself) example 2*3 = 6 6/2 = 3 3^2 = 9 ( means multiply 3 by itself twice)

Question:Hi. I have a math problem here...I have the answer to it, so you don't need to solve anything: -21+q<19 Apparently, the answer is {q|q<40} My questions are: Why are they in squiggly brackets and what is the line in the middle of the two q's? What do they mean and when do I need them? Thanks so much!

Answers:It's just a format in which to write solutions in, and it's called set-builder notation: http://www.mathwords.com/s/set_builder_notation.htm . The answer is simply q < 40, but in set builder notation it is written as {q | q < 40}.

Question:its sorta a squiggly x its usually next to a number. I don't mean multiplication, its in my algebra book and i seemed to have missed learning that -__- here's an example if someone could explain it to me? 5x + 2x = 35 i dont get it ^^;;; How do you solve the problem?

Answers:It is like you have 5 apple and 2 apple. X is a variable like apple or anything. The coefficient in front of the x shows you how many "x" you have. Here you have 5+2 = 7 apple and Let say 7 apple is 35$, then one apple is 5$. Use math this means that ; x=5.

From Youtube

math in mean girls :1 I like math In this first clip, we are given a glimpse in to Kady's character through her voicing of a common strength of mathematics: universality. Why is this claim plausible? What might we get out of understanding it more thoroughly? 2 invitation to mathletes here we see the social dichotomy emerge between coolness and math. We also have the exception-proving-the-rule Kevin. Mathematicians tend to be shy introverts. Discuss. 3 talking to aaron As Kady gives in to the dark side, math is used here as a symbol for her personal integrity 4 talking and tutoring Here we see Kady in the depth of self-denial, choosing to fail her math tests/quizzes in order to get more face time with Aaron. The narrative voice is almost, but not quite her conscience. Notice the focus on wrong versus right answers portrayed as the natural focus point for a math discussion. 5 just the answers are wrong Ms. Norberry has Kady figured out. Not only is Kady poor at covering up her intelligence, the teacher feels justified in giving her poor marks for correct work but incorrect answers. 6 righteous path More math as a convenient symbol for the heroine's return to the righteous path. "Welcome back, nerd!" 7 math contest The math contest is full of math stereotypes. Maybe a list is in order. My favorite one to notice is the crowd. Not only is it sparser than Kevin's "good turnout this year", there aren't even enough people in attendance to account for the parents of the participants. 8 final battle ...