Are they irrational? Transcendental? | Epic Math Time скачать в хорошем качестве

Are they irrational? Transcendental? | Epic Math Time

Showing that a number is transcendental can be difficult. While π and e have a deep connection involving exponentiation, other combinations of them, like π + e, are not as well understood. Follow me on Instagram for previews, behind-the-scenes, and more content!:   / epicmathtime   Special thanks to my Channel Supporters: Dru Vitale, RYAN KUEMPER, AlkanKondo89, John Patterson, Johann, Speedy, Zach Ager, and Joseph Wofford. Click the blue "Join" button to see how you can support the channel. Definitions: Algebraic number: A number that is a root of some polynomial with integer coefficients. Examples include 42 (a root of x - 42), √2 (a root of x² - 2), φ (The Golden Ratio, a root of x² - x - 1). All rational numbers r = p/q are algebraic, because they are always the root of the equation qx - p. Irrational numbers can also be algebraic, such as the example of √2 above. Transcendental number: A number that is not algebraic. Examples include π, e, cos(1), etc. The usual transcendental numbers that one encounters cannot be expressed in terms of finitely many operations on integers. Practically speaking, this is why they often get their own symbol and name, like π, as any other way to express them (such as an infinite sum of rational numbers) is cumbersome. Music: Reflection, Fear Inoculum, Lateralus originally by Tool, as performed by Sakis Strigas:    / tbird4pro   My current equipment for making videos (affiliate links): Camera: https://amzn.to/2HSJXDR Microphone(s): https://amzn.to/2SnpWY5 Audio Interface: https://amzn.to/3fcjMoc