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GF(2) is the only field with this property (Proof: if x 2 = x, then either x = 0 or x ≠ 0. In the latter case, x must have a multiplicative inverse, in which case dividing both sides by x gives x = 1. All larger fields contain elements other than 0 and 1, and those elements cannot satisfy this property).
In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field.
A record is a value that contains other values, typically in fixed number and sequence and typically indexed by names. The elements of records are usually called fields or members. An object contains a number of data fields, like a record, and also offers a number of subroutines for accessing or modifying them, called methods.
A data field holds a single fact or attribute of an entity. Consider a date field, e.g. "19 September 2004". This can be treated as a single date field (e.g. birthdate), or three fields, namely, day of month, month and year. A record is a collection of related fields. An Employee record may contain a name field(s), address fields, birthdate ...
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Finite fields (also called Galois fields) are fields with finitely many elements, whose number is also referred to as the order of the field. The above introductory example F 4 is a field with four elements. Its subfield F 2 is the smallest field, because by definition a field has at least two distinct elements, 0 and 1.
Forecasts for 2014’s races for governor, based on HuffPost Pollster’s poll-tracking model 06/19 Hospice, Inc. A Huffington Post investigation into the business of dying
CNN asked convicted felons about their struggles, their hopes and how they feel about President-elect Donald Trump, who will return to the White House after being convicted of 34 felony charges.