Show that Q, the set of all rational numbers, is dense along the number line by showing that given any two rational line by showing that given any two rational numbers
To prove:
Along the number line, the set
Given information:
Concept used:
The set of rational number is defined as follows.
The set rational number can also be written as
Proof:
Let
Now show that there exists a rational number between
The midpoint between any two numbers on the number line is its average.
That means the midpoint for the numbers
That means
The number
Let
Let