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Number Definition & Meaning A tallying system has no concept of place value , which limits its representation of large numbers. Nonetheless, tallying systems are considered the first kind of abstract numeral system. The numerator and denominator values should be instances of Integral and should be in lowest terms withdenominator positive. The first existence proofs of irrational numbers is usually attributed to Pythagoras, more specifically to the Pythagorean Hippasus of Metapontum, who produced a proof of the irrationality of the square root of 2. The story goes that Hippasus discovered irrational numbers when trying to represent the square root of 2 as a fraction. However, Pythagoras believed in the absoluteness of numbers, and could not accept the existence of irrational numbers. The first known documented use of zero dates to AD 628, and appeared in the Brāhmasphuṭasiddhānta, the main work of the Indian mathematician Brahmagupta. He treated 0 as a number and discussed oper...