## From zero to infinity: what makes numbers interesting |

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aleph aleph-null aleph-one answer arithmetic base-sixteen beads bers binary system Cantor cardinal number Carl Friedrich Gauss casting out nines century column composite numbers congruence x2 constructible polygons counting board decimal fraction decimal system digits Diophantus divide divisible divisors equal Euclid Euler expressed fact Fermat numbers Fermat primes five G. H. Hardy Galileo Gauss Georg Cantor Greeks infinite number infinite set infinity interesting number large number mathematicians mathematics Mersenne number Mersenne prime method mod 9 natural numbers nine cubes number of cubes number of numbers number of primes number representation number theory numbers requiring odd number one-to-one correspondence pair pentagonal numbers perfect numbers Pierre Fermat placed in one-to-one polygonal numbers positive integers powers of three prime factors prime numbers produce proof proved Quadratic Reciprocity question rational number reader relationship represent all numbers seven simply solvable SWAC symbol theory of numbers tion transfinite cardinal unique Waring's Problem whole number Wilson's Theorem