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These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
Fixtures practically constitute the arrange phase in the anatomy of a test (AAA, short for arrange, act, assert). [11] [10] Pytest fixtures can run before test cases as setup or after test cases for clean up, but are different from unittest and nose (another third-party Python testing framework)'s setups and teardowns.
In computer programming, specifically when using the imperative programming paradigm, an assertion is a predicate (a Boolean-valued function over the state space, usually expressed as a logical proposition using the variables of a program) connected to a point in the program, that always should evaluate to true at that point in code execution.
An empty set exists. This formula is a theorem and considered true in every version of set theory. The only controversy is over how it should be justified: by making it an axiom; by deriving it from a set-existence axiom (or logic) and the axiom of separation; by deriving it from the axiom of infinity; or some other method.
In some programming language environments (at least one proprietary Lisp implementation, for example), [citation needed] the value used as the null pointer (called nil in Lisp) may actually be a pointer to a block of internal data useful to the implementation (but not explicitly reachable from user programs), thus allowing the same register to be used as a useful constant and a quick way of ...
In computer software testing, a test assertion is an expression which encapsulates some testable logic specified about a target under test. The expression is formally presented as an assertion, along with some form of identifier, to help testers and engineers ensure that tests of the target relate properly and clearly to the corresponding specified statements about the target.
As a result, the empty set is the unique initial object of the category of sets and functions. The empty set can be turned into a topological space, called the empty space, in just one way: by defining the empty set to be open. This empty topological space is the unique initial object in the category of topological spaces with continuous maps.
Gödel noted that each statement within a system can be represented by a natural number (its Gödel number).The significance of this was that properties of a statement—such as its truth or falsehood—would be equivalent to determining whether its Gödel number had certain properties.