String (computer science) in the context of "Logical form"

In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".

The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called well-formed words. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar.

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess."

According to formalism, mathematical statements are not "about" numbers, sets, triangles, or any other mathematical objects in the way that physical statements are about material objects. Instead, they are purely syntactic expressions—formal strings of symbols manipulated according to explicit rules without inherent meaning. These symbolic expressions only acquire interpretation (or semantics) when we choose to assign it, similar to how chess pieces follow movement rules without representing real-world entities. This view stands in stark contrast to mathematical realism, which holds that mathematical objects genuinely exist in some abstract realm.

Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). The term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network). Most such notions of distance, both physical and metaphorical, are formalized in mathematics using the notion of a metric space.

In the social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance.

In logic, syntax is an arrangement of well-structured entities in the formal languages or formal systems that express something. Syntax is concerned with the rules used for constructing or transforming the symbols and words of a language, as contrasted with the semantics of a language, which is concerned with its meaning.

The symbols, formulas, systems, theorems and proofs expressed in formal languages are syntactic entities whose properties may be studied without regard to any meaning they may be given, and, in fact, need not be given any.

In a positional numeral system, the radix (pl. radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9.

In any standard positional numeral system, a number is conventionally written as (x)_y with x as the string of digits and y as its base. For base ten, the subscript is usually assumed and omitted (together with the enclosing parentheses), as it is the most common way to express value. For example, (100)₁₀ is equivalent to 100 (the decimal system is implied in the latter) and represents the number one hundred, while (100)₂ (in the binary system with base 2) represents the number four.

A serial number (SN) is a unique identifier used to uniquely identify an item, and is usually assigned incrementally or sequentially.

Despite being called serial "numbers", they do not need to be strictly numerical and may contain letters and other typographical symbols, or may consist entirely of a character string.

In computing and telecommunications, a character is the encoded representation of a natural language character (including letter, numeral and punctuation), whitespace (space or tab), or a control character (controls computer hardware that consumes character-based data). A sequence of characters is called a string.

Some character encoding systems represent each character using a fixed number of bits whereas other systems use varying sizes. Various fixed-length sizes were used for now obsolete systems such as the six-bit character code, the five-bit Baudot code and even 4-bit systems (with only 16 possible values). The more modern ASCII system uses the 8-bit byte for each character. Today, the Unicode-based UTF-8 encoding uses a varying number of byte-sized code units to define a code point which combine to encode a character.