Number fields

Number fields are specific sets of numbers constructed by taking rational numbers (fractions) and adding solutions to polynomial equations that have coefficients in the rationals. Essentially, they are extended systems that include numbers like roots of algebraic equations, such as √2 or complex numbers like i. These fields help mathematicians study relationships and properties of algebraic numbers, providing a framework for understanding solutions to polynomial problems and the structure of numbers beyond rationals. They are fundamental in areas like algebra, number theory, and cryptography, offering a systematic way to analyze complex numerical relationships.