GF(2)

$GF(2)$ (also denoted $\mathbb {F} _{2}$ , $Z /2 Z$ or $\mathbb {Z} /2\mathbb {Z}$ ) is the finite field with two elements.^[1]^[a]

$GF(2)$ is the field with the smallest possible number of elements, and is unique if the additive identity and the multiplicative identity are denoted respectively 0 and 1, as usual.

The elements of $GF(2)$ may be identified with the two possible values of a bit and to the boolean values true and false. It follows that $GF(2)$ is fundamental and ubiquitous in computer science and its logical foundations.

^ Lidl, Rudolf; Niederreiter, Harald (1997). Finite fields. Encyclopedia of Mathematics and Its Applications. Vol. 20 (2nd ed.). Cambridge University Press. ISBN 0-521-39231-4. Zbl 0866.11069.

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[1] Lidl, Rudolf; Niederreiter, Harald (1997). Finite fields. Encyclopedia of Mathematics and Its Applications. Vol. 20 (2nd ed.). Cambridge University Press. ISBN 0-521-39231-4. Zbl 0866.11069.

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