29 сент. 2015 г. · Proof: You have a/b - c/d with a,b,c,d being integers and b,d not equal to 0. ... Thus a/b - c/d is a rational number. ... Yep that's right.

26 янв. 2015 г. · The product of two integers is an integer; the difference of two integers is an integer; a rational is defined as one integer divided by another non-zero ...

30 апр. 2018 г. · Your proof is correct. A similar approach is just taking the average of the two rational numbers (which is again a rational number).

16 окт. 2014 г. · The exercise I am working on is about proving whether there is always a rational number between two other distinct rational numbers.

7 апр. 2015 г. · It may not always be the case that the difference between two irrational numbers is rational. Nonetheless, the sum x+y of an irrational number,y ...

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.

12 июн. 2012 г. · The short answer to your question is that is not necessarily true. For instance, √2,√2−1,1−√2 are all irrational but √2+(1−√2)=1∈Q.

28 окт. 2013 г. · Look at the contrapositive: If x is rational, then x+n is rational. Clearly this is a true statement.

26 мар. 2012 г. · The answer, in a nutshell: real numbers correspond to sets of rationals rather to rationals, and there are a lot more sets than rationals.

9 дек. 2012 г. · The difference between rational and irrational numbers is always stated as: rational numbers can be written as the ratio of two integers, and irrational ...