Jun 13, 2012 · 3 Sum of two irrationals can be rational or irrational. Example for sum of two irrationals being irrational $\sqrt {2}$ is irrational. $\sqrt {2} + \sqrt {2} = 2 \sqrt {2}$ which is …

Jun 23, 2015 · $\\mathbb Q$ is used to represent rational numbers. $\\mathbb R$ is used to represent reals. Is there a symbol or convention that represents irrationals. Possibly $\\mathbb …

I tried 'Proof by Contraposition'. Product of two irrational number is irrational. p : Product of two irrational number q : Irrational number. Thus, given statement is : p -> q Contraposition of p : …

Oct 29, 2013 · I had a little back and forth with my logic professor earlier today about proving a number is irrational. I proposed that 1 + an irrational number is always irrational, thus if I could …

The proof for $\log_ {2}3$ is a nice example, by the way. Peter, you should look at Ivan Niven's book Numbers: Rational and Irrational.

Jan 27, 2015 · I'm being asked to prove that the set of irrational number is dense in the real numbers. While I do understand the general idea of the proof: Given an interval $ (x,y)$, …

Jul 8, 2021 · Any irrational number has a non-terminating, non-repeating sequence of digits in its decimal representation (or the representation in any whole number base). This is easy to …

Sep 15, 2015 · A real number is irrational if and only if it is not rational. By definition any real number is either rational or irrational. I suppose the creator of this image chose this …

May 22, 2015 · To show that the set of irrational number is not closed under ordinary multiplication, I seek a counter-example that is $$\sqrt {2} \times \sqrt {2} = 2 = \frac {2} {1}$$ …

Possible Duplicate: Density of irrationals 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 tw...