irrational

(adjective)

of a real number, that cannot be written as the ratio of two integers

Related Terms

Examples of irrational in the following topics:

  • Real Numbers, Functions, and Graphs

    • The real numbers include all the rational numbers, such as the integer -5 and the fraction $\displaystyle \frac{4}{3}$, and all the irrational numbers such as $\sqrt{2}$ (1.41421356… the square root of two, an irrational algebraic number) and $\pi$ (3.14159265…, a transcendental number).

  • The Natural Logarithmic Function: Differentiation and Integration

    • The natural logarithm, generally written as $\ln(x)$, is the logarithm with the base e, where e is an irrational and transcendental constant approximately equal to $2.718281828$.

  • Intermediate Value Theorem

    • However there is no rational number $x$ such that $f(x) =0$, because $\sqrt 2$ is irrational.