Juxtaposition
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.
Speech
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. 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". Piaget writes: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, many languages use simple juxtaposition. 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.
Mathematics
In algebra, multiplication involving variables is often written as a juxtaposition, also called implied multiplication. The notation can also be used for quantities that are surrounded by parentheses. 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, 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.