(loosely) a mathematical function such that a small change in the independent variable, or point of the domain, produces only a small change in the value of the function.
(at a point in its domain) a function that has a limit equal to the value of the function at the point; a function that has the property that for any small number, a second number can be found such that when the distance between any other point in the domain and the given point is less than the second number, the difference in the functional values at the two points is less than the first number in absolute value.
(at a point in a topological space) a function having the property that for any open set containing the image of the point, an open set about the given point can be found such that the image of the set is contained in the first open set.
(on a set in the domain of the function or in a topological space) a function that is continuous at every point of the set.
Continually vs. ContinuouslyToday we’re going to explore the meanings and uses of the adverbs continually and continuously. These terms, along with their adjective forms continual and continuous, are often used interchangeably in speech and writing, but style guides urge writers to practice discernment when using continually and continuously. In formal contexts, continually should be used to mean “very often; at regular or frequent intervals,” and continuously to …
Present, Past, And Sometimes Perfect ParticiplesParticiples are words derived from verbs that can function as adjectives or as parts of verb phrases to create verb tenses. The two main types of participles are the present participle and the past participle. The perfect participle depends on the past participle for its forms. Participial phrases function as adjectives that modify the subjects or other nouns in sentences. The Present Participle Adding -ing …
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019