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Benito Santiago, a Major League Baseball catcher who wore the number 09 for several years, is the only major professional sports league player to use a jersey number with a leading zero, not counting several who have worn the number 00 (he wore the extra zero to avoid complications with his catcher's pads, allowing the back strap to run between ...
The number field Q(√2) sits inside R, and the two embeddings of the field into C send every element in the field to another element of R, hence the field is totally real. In number theory, a number field F is called totally real if for each embedding of F into the complex numbers the image lies inside the real numbers.
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers , finite fields , and function fields .
The origins of class field theory lie in the quadratic reciprocity law proved by Gauss. The generalization took place as a long-term historical project, involving quadratic forms and their 'genus theory', work of Ernst Kummer and Leopold Kronecker/Kurt Hensel on ideals and completions, the theory of cyclotomic and Kummer extensions.
A real number can be expressed by a finite number of decimal digits only if it is rational and its fractional part has a denominator whose prime factors are 2 or 5 or both, because these are the prime factors of 10, the base of the decimal system. Thus, for example, one half is 0.5, one fifth is 0.2, one-tenth is 0.1, and one fiftieth is 0.02.
Service numbers (area codes 800, 900, 906 and 909) have either 4 or 7 remaining digits, making them 8 or 11 digits in total: 0AAA-BBBB or 0AAA-BBBBBBB. The area code 14 has no trunk prefix and is used for government numbers, currently only for municipalities. The remaining digits represent the area code of the municipality.
A finite field of order exists if and only if is a prime power (where is a prime number and is a positive integer). In a field of order p k {\displaystyle p^{k}} , adding p {\displaystyle p} copies of any element always results in zero; that is, the characteristic of the field is p {\displaystyle p} .
The progressions of numbers that are 0, 3, or 6 mod 9 contain at most one prime number (the number 3); the remaining progressions of numbers that are 2, 4, 5, 7, and 8 mod 9 have infinitely many prime numbers, with similar numbers of primes in each progression.