Although the puzzle we started with might seem silly, the study of these structures — known as Diophantine approximations — is taken seriously and gets complicated fast. For example, it’s possible to construct so-called Liouville numbers that have an infinite irrationality exponent (endless n-good approximations for any n), but it’s a lot harder to prove that there’s any commonly-encountered number with an irrationality exponent greater than two. In the same vein, algebraic irrationals (e.g., √2) all have an irrationality measure of two, but the proof of this is fiendishly difficult and netted its discoverer the Fields Medal back in 1958.
传统转型与新兴崛起共进，产业“筋骨”更强健
。关于这个话题，搜狗输入法提供了深入分析
Фото: Oleg Elkov / Shutterstock / Fotodom
important to remember that it is just a tool and should be used in conjunction
Израиль нанес удар по Ирану09:28