16 июн. 2013 г. · Yes, there is. This is known as the "density of the rationals in the reals", which says in fact that between any two reals numbers there is a rational number.

24 июл. 2016 г. · A quick and inelegant approach is to use the (beginnings of the) decimal expansions √ 2 =1.41... and √ 3 =1.73... . Any terminating decimal between these two ...

6 сент. 2016 г. · In this case the arithmetic mean x+y2 is always an irrational number between x and y. Also, if y is irrational then it has a non-terminating ...

18 июл. 2017 г. · There is a rational number between two irrational numbers, and an irrational number between two rational numbers. So what's between an ...

16 янв. 2015 г. · I'm trying to prove that there is an irrational number between any two unequal rational numbers a,b. Here's a proof I have right now, but I'm not sure if it ...

2 дек. 2011 г. · There is an irrational number in (a,b) since the rationals themselves are countable. If α is irrational then rα is irrational and n+α is ...

2 нояб. 2015 г. · Thus k<(n−m), x+k is irrational and m<x<(x+k)<n. For example, let's say we have found √7 is an irrational number between 2 and 3.

30 апр. 2018 г. · The difference between the two numbers is a rational number. Two multiplied rationals has a rational product, and so if we multiply the ( ...

12 янв. 2018 г. · This proof is showing is how much our intuitions about the real numbers and integers are related to the Archimedean property.

15 сент. 2019 г. · Here's a theorem for you: Between any two real numbers there is a rational. This fact is a jumping off point from your very second line.