Juxtaposition is an act or instance of placing two opposing elements close together or side by side. This is often done in order to compare/contrast the two, to show similarities or differences, etc.
Juxtaposition is an act or instance of placing two opposing elements close together or side by side. This is often done in order to compare/contrast the two, to show similarities or differences, etc.
Juxtaposition in literary terms is the showing contrast by concepts placed side by side. An example of juxtaposition are the quotes "Ask not what your country can do for you; ask what you can do for your country", and "Let us never negotiate out of fear, but let us never fear to negotiate", both by John F. Kennedy, who particularly liked juxtaposition as a rhetorical device. [1] Jean Piaget specifically contrasts juxtaposition in various fields from syncretism, arguing that "juxtaposition and syncretism are in antithesis, syncretism being the predominance of the whole over the details, juxtaposition that of the details over the whole". [2] Piaget writes:
In visual perception, juxtaposition is the absence of relations between details; syncretism is a vision of the whole which creates a vague but all-inclusive schema, supplanting the details. In verbal intelligence juxtaposition is the absence of relations between the various terms of a sentence; syncretism is the all-round understanding which makes the sentence into a whole. In logic juxtaposition leads to an absence of implication and reciprocal justification between the successive judgments; syncretism creates a tendency to bind everything together and to justify by means of the most ingenious or the most facetious devices. [2]
In grammar, juxtaposition refers to the absence of linking elements in a group of words that are listed together. Thus, where English uses the conjunction and (e.g. mother and father), many languages use simple juxtaposition ("mother father"). In logic, juxtaposition is a logical fallacy on the part of the observer, where two items placed next to each other imply a correlation, when none is actually claimed. For example, an illustration of a politician and Adolf Hitler on the same page would imply that the politician had a common ideology with Hitler. Similarly, saying "Hitler was in favor of gun control, and so are you" would have the same effect. This particular rhetorical device is common enough to have its own name, Reductio ad Hitlerum.
In algebra, multiplication involving variables is often written as a juxtaposition (e.g., for times or for five times ), also called implied multiplication. [3] The notation can also be used for quantities that are surrounded by parentheses (e.g., or for five times two). This implicit usage of multiplication can cause ambiguity when the concatenated variables happen to match the name of another variable, when a variable name in front of a parenthesis can be confused with a function name, or in the correct determination of the order of operations.
In mathematics, juxtaposition of symbols is the adjacency of factors with the absence of an explicit operator in an expression, especially for commonly used for multiplication: denotes the product of with , or times . It is also used for scalar multiplication, matrix multiplication, function composition, and logical and. In numeral systems, juxtaposition of digits has a specific meaning. In geometry, juxtaposition of names of points represents lines or line segments. In lambda calculus, juxtaposition denotes function application. In physics, juxtaposition is also used for "multiplication" of a numerical value and a physical quantity, and of two physical quantities, for example, three times would be written as and "area equals length times width" as .
Throughout the arts, juxtaposition of elements is used to elicit a response within the audience's mind, such as creating meaning from the contrast. In music, it is an abrupt change of elements, and is a procedure of musical contrast. In film, the position of shots next to one another (montage) is intended to have this effect. In painting and photography, the juxtaposition of colours, shapes, etc, is used to create contrast, while the position of particular kinds of objects one upon the other or different kinds of characters in proximity to one another is intended to evoke meaning. [4] Various forms of juxtaposition occur in literature, where two images that are otherwise not commonly brought together appear side by side or structurally close together, thereby forcing the reader to stop and reconsider the meaning of the text through the contrasting images, ideas, motifs, etc. For example, "He was slouched gracefully" is a juxtaposition. More broadly, an author can juxtapose contrasting types of characters, such as a hero and a rogue working together to achieve a common objective from very different motivations. [4]
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
In mathematics, the associative property is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.
In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.
Elementary algebra, also known as college algebra, encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, whilst algebra introduces variables.
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics.
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. Equality between A and B is written A = B, and pronounced "A equals B". In this equality, A and B are distinguished by calling them left-hand side (LHS), and right-hand side (RHS). Two objects that are not equal are said to be distinct.
In mathematics, an algebraic structure consists of a nonempty set A, a collection of operations on A, and a finite set of identities that these operations must satisfy.
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more advanced settings. The name is needed because there are operations, such as division and subtraction, that do not have it ; such operations are not commutative, and so are referred to as noncommutative operations. The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric if the relation applies regardless of the order of its operands; for example, equality is symmetric as two equal mathematical objects are equal regardless of their order.
In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can denote numbers, variables, operations, and functions. Other symbols include punctuation marks and brackets, used for grouping where there is not a well-defined order of operations.
In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x^2 (caret) or x**2 may be used in place of x2. The adjective which corresponds to squaring is quadratic.
Parataxis is a literary technique, in writing or speaking, that favors short, simple sentences, without conjunctions or with the use of coordinating, but not with subordinating conjunctions. It contrasts with syntaxis and hypotaxis.
A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of an integer numerator, displayed above a line, and a non-zero integer denominator, displayed below that line. If these integers are positive, then the numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole. The picture to the right illustrates 3/4 of a cake.
In mathematical logic, a tautology is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. For example, a formula that states, "the ball is green or the ball is not green," is always true, regardless of what a ball is and regardless of its colour. Tautology is usually, though not always, used to refer to valid formulas of propositional logic.
In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables. The constants of a language can further be divided into logical symbols and non-logical symbols.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication.
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion.
In mathematical logic, a term denotes a mathematical object while a formula denotes a mathematical fact. In particular, terms appear as components of a formula. This is analogous to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact.
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier in the first order formula expresses that everything in the domain satisfies the property denoted by . On the other hand, the existential quantifier in the formula expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable.
The dictionary definition of juxtaposition at Wiktionary
