Скачать с ютуб Discontinuity (mathematics) | Wikipedia audio article в хорошем качестве

Discontinuity (mathematics) | Wikipedia audio article

This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Classif... 00:00:36 1 Classification 00:01:13 1.1 Removable discontinuity 00:01:50 1.2 Jump discontinuity 00:02:26 1.3 Essential discontinuity 00:03:03 2 The set of discontinuities of a function 00:03:58 3 See also 00:04:35 4 Notes Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: increases imagination and understanding improves your listening skills improves your own spoken accent learn while on the move reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services... Other Wikipedia audio articles at: https://www.youtube.com/results?searc... Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts Speaking Rate: 0.9613760489933056 Voice name: en-US-Wavenet-E "I cannot teach anybody anything, I can only make them think." Socrates SUMMARY ======= 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. This article describes the classification of discontinuities in the simplest case of functions of a single real variable taking real values. 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.limit is constantA 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).