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Irrational Numbers

Summary

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Rational Numbers:
Numbers that can be written in the form of $\frac{\text{p}}{\text{q}}$, where p, q are integers and q ≠ 0. The collection of Rational numbers is denoted by Q. Between any two rational numbers there exists infinitely many rational numbers.

Irrational numbers:
Numbers which cannot be expressed in the form of $\frac{\text{p}}{\text{q}}$, where p and q are integers and q ≠ 0.
The collection of irrational numbers is denoted by $\stackrel{_}{\text{Q}}$.

Pythagoras Theorem:
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Irrational numbers can be represented on the number line using Pythagoras theorem.

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