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. · In general, we may assume to have two distinct irrational numbers a,b with their difference, multiplied by some n∈N, being greater than one.

8 сент. 2015 г. · Suppose r=ab with coprime positive integers a,b. Then, we get 2ab=3. Take the b−th power on both sides. 2a=3b.

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. · I am trying to prove that there exists an irrational number between any two real numbers a and b. I already know that a rational number between the two of them ...

12 нояб. 2016 г. · In particular, for your question: It is not possible to have two different irrationals that don't have any rational number between them. Share.

20 февр. 2014 г. · You can complete the square, discover (what you could have found from the quadratic formula) the roots involve √5 and prove √5 is irrational. – ...

19 мая 2024 г. · There is also an infinite number of rationals between any two irrationals. Only a countable infinite number, but certainly more than two. More ...

4 февр. 2013 г. · So if there exists a rational number equal to √2, there must also exist a rational number in lowest terms equal to √2. Share.

5 окт. 2020 г. · Prove that there is no rational number ... Prove that there is an irrational number and a rational number between any two distinct real numbers.