Translation and analysis of words by ChatGPT artificial intelligence
On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:
- how the word is used
- frequency of use
- it is used more often in oral or written speech
- word translation options
- usage examples (several phrases with translation)
- etymology
What (who) is jump point - definition
Wikipedia
Continuous functions are of utmost importance in mathematics, functions and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function.
The oscillation of a function at a point quantifies these discontinuities as follows:
- in a removable discontinuity, the distance that the value of the function is off by is the oscillation;
- in a jump discontinuity, the size of the jump is the oscillation (assuming that the value at the point lies between these limits of the two sides);
- in an essential discontinuity, oscillation measures the failure of a limit to exist; the limit is constant.
A special case is if the function diverges to infinity or minus infinity, in which case the oscillation is not defined (in the extended real numbers, this is a removable discontinuity).
