For example, while an analog speedometer can theoretically display an infinite number of speeds, digital speedometers generally display speeds in whole numbers.
The ancient Egyptians developed a powerful system of numerals with distinct hieroglyphs for 1, 10, and all the powers of 10 up to over 1 million.
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However, 0 had been used as a number in the medieval computus (the calculation of the date of Easter), beginning with Dionysius Exiguus in 525, without being denoted by a numeral (standard Roman numerals do not have a symbol for 0); instead nulla or nullae, genitive of nullus, the Latin word for "none", was employed to denote a 0 value.
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In 1922, Fraenkel and Skolem pointed out that Zermelo's axioms cannot prove the existence of the set {Z0, Z1, Z2, … } where Z0 is the set of natural numbers, and Zn+1 is the power set of Zn.
Büchi arithmetic of base k is the first-order theory of the natural numbers with addition and the function which is defined as the bigger power of k dividing x, named in honor of the Swiss mathematician Julius Richard Büchi.
The rejection of impredicatively defined mathematical objects (while accepting the natural numbers as classically understood) leads to the position in the philosophy of mathematics known as predicativism, advocated by Henri Poincaré and Hermann Weyl in his Das Kontinuum.
Finite set, whose cardinality (number of elements) is some natural number
Riesel number, an odd natural number k for which the integers of the form k·2n−1 are all composite
Waring's problem asks whether for every natural number k there exists an associated positive integer s such that every natural number is the sum of at most s kth powers of natural numbers.