In mathematics, the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length, no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.

अपरिमेय संख्या' ज्या संख्या भौमितिक प्रतलावर अचूक मांडता येत नाहीत, त्यांना अपरिमेय संख्या म्हणतात. या संख्या अंश भागिले छेद अशा लिहिता येत नाहीत, किंवा दशांश पद्धतीत लिहिल्या असता त्यांतील आकड्यांचा क्रम कोणताही नियम पाळत नाही.