Irrational Number

In <a href="https://en.wikipedia.org/wiki/Mathematics" title="Mathematics" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: "Helvetica Neue", Helvetica, "Nimbus Sans L", Arial, "Liberation Sans", sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(255, 255, 255); color: rgb(90, 54, 150);">mathematics</a>, the <b style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: "Helvetica Neue", Helvetica, "Nimbus Sans L", Arial, "Liberation Sans", sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; color: rgb(34, 34, 34);">irrational numbers are all the <a href="https://en.wikipedia.org/wiki/Real_number" title="Real number" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: "Helvetica Neue", Helvetica, "Nimbus Sans L", Arial, "Liberation Sans", sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(255, 255, 255); color: rgb(90, 54, 150);">real numbers</a> which are not <a href="https://en.wikipedia.org/wiki/Rational_number" title="Rational number" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: "Helvetica Neue", Helvetica, "Nimbus Sans L", Arial, "Liberation Sans", sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(255, 255, 255); color: rgb(90, 54, 150);">rational numbers</a>, the latter being the numbers constructed from ratios (or <a href="https://en.wikipedia.org/wiki/Fraction(mathematics)" title="Fraction (mathematics)" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: "Helvetica Neue", Helvetica, "Nimbus Sans L", Arial, "Liberation Sans", sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(255, 255, 255); color: rgb(90, 54, 150);">fractions</a>) of <a href="https://en.wikipedia.org/wiki/Integer" title="Integer" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: "Helvetica Neue", Helvetica, "Nimbus Sans L", Arial, "Liberation Sans", sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(255, 255, 255); color: rgb(90, 54, 150);">integers</a>. When the <a href="https://en.wikipedia.org/wiki/Ratio" title="Ratio" style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: "Helvetica Neue", Helvetica, "Nimbus Sans L", Arial, "Liberation Sans", sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: rgb(255, 255, 255); color: rgb(90, 54, 150);">ratio</a> of lengths of two line segments is an irrational number, the line segments are also described as being <i style="margin: 0px; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: "Helvetica Neue", Helvetica, "Nimbus Sans L", Arial, "Liberation Sans", sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; color: rgb(34, 34, 34);"><a href="https://en.wikipedia.org/wiki/Commensurability(mathematics)" title="Commensurability (mathematics)" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background-image: none; background-position: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: initial; color: rgb(90, 54, 150);">incommensurable</a>, meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.