In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics. In type theory, every "term" has a "type" and operations are restricted to terms of a certain type.
Type theory is closely related to (and in some cases overlaps with) type systems, which are a programming language feature used to reduce bugs. The types of type theory were created to avoid paradoxes in a variety of formal logics and rewrite systems and sometimes "type theory" is used to refer to this broader application.
In physics, assuming a flat Earth with a uniform gravity field, and no air resistance, a projectile launched with specific initial conditions will have a predictable range.
The following applies for ranges which are small compared to the size of the Earth. For longer ranges see sub-orbital spaceflight.
In programming languages, a type system is a collection of rules that assign a property called a type to the various constructs—such as variables, expressions, functions or modules—a computer program is composed of. The main purpose of a type system is to reduce bugs in computer programs by defining interfaces between different parts of a computer program, and then checking that the parts have been connected in a consistent way. This checking can happen statically (at compile time), dynamically (at run time), or as a combination thereof.
An example of a simple type system is that of the C language. The portions of a C program are the function definitions. One function is invoked by another function. The interface of a function states the name of the function and a list of values that are passed to the function's code. The code of an invoking function states the name of the invoked, along with the names of variables that hold values to pass to it. During execution, the values are placed into temporary storage, then execution jumps to the code of the invoked function. The invoked function's code accesses the values and makes use of them. If the instructions inside the function are written with the assumption of receiving an integer value, but the calling code passed a floating-point value, then the wrong result will be computed by the invoked function. The C compiler checks the type declared for each variable sent, against the type declared for each variable in the interface of the invoked function. If the types do not match, the compiler throws a compile-time error.
In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word (i.e. a finite sequence of symbols from a given alphabet) which is part of a formal language. A formal language can be considered to be identical to the set containing all and only its formulas.
A formula is a syntactic formal object that can be informally given a semantic meaning.
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 the numbers 0, 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.
A mathematical notation is a writing system used for recording concepts in mathematics.
In journalism, a human interest story is a feature story that discusses a person or people in an emotional way. It presents people and their problems, concerns, or achievements in a way that brings about interest, sympathy or motivation in the reader or viewer.
Human interest stories may be "the story behind the story" about an event, organization, or otherwise faceless historical happening, such as about the life of an individual soldier during wartime, an interview with a survivor of a natural disaster, a random act of kindness or profile of someone known for a career achievement.