# Numbers

#### Examples of Irrational Numbers (With Lists)

Have you ever wondered how to create an irrational number? There are infinite irrational numbers between any two rational numbers, yet they are difficult to find. No list enumerates all the irrational numbers. There are more irrational numbers than rational ... more

#### Product of rational & irrational numbers is irrational (Proof + Questions)

Proof We prove this by contradiction. Let yx​ be a rational number and p an irrational number. Let us assume that product of these numbers is a rational number ba​. We are hoping to get a contradiction due to this assumption. The assumption results in the ... more

#### Square root of a Prime (5) is Irrational (Proof + Questions)

This proof works for any prime number: 2, 3, 5, 7, 11, etc. Let’s prove for 5. First, we will assume that the square root of 5 is a rational number. Next, we will show that our assumption leads to a contradiction. Let us assume √5 is a rational ... more

#### Sum of rational & irrational numbers (Proof, Examples)

Proof We will prove this by contradiction. Let us add a rational number ( =yx​), to an irrational number ( = p ). We assume that the result is a rational number ( =ba​ ). Putting these in an equation, we get: yx​+p=ba​ p=ba​−yx​ p=byay−xb​ ... more