# Mathematical Notation

The following notation is used throughout the text:

N | The set of natural numbers `N = {1, 2, 3 ...}`.
Z | The set of integers `Z = {... -3, -2, -1, 0, 1, 2, 3 ...}`.
R | The set of real numbers.
| The floor of a (the largest integer less than or equal to a).
⊕ or xor | Bitwise exclusive OR.
| Binomial coefficient or combination `(α∈R, α≥ 0; k∈N ∪{0}).` For `α≥k` binomial coefficient is defined as If `α < k`, then
`Φ(x)` | Cumulative Gaussian distribution function defined over `- ∞ < x < + ∞.` `Φ(-∞) = 0, Φ(+∞) = 1`.
`Γ(α)` | The complete gamma function where `α > 0`.
B(p, q) | The complete beta function where `p>0` and `q>0`.
LCG(a,c, m) | Linear Congruential Generator `xn+1 = (axn + c) mod m`, where a is called the multiplier, c is called the increment, and m is called the modulus of the generator.
MCG(a,m) | Multiplicative Congruential Generator `xn+1 = (axn) mod m` is a special case of Linear Congruential Generator, where the increment c is taken to be 0.
GFSR(p, q) | Generalized Feedback Shift Register Generator `xn = xn-p ⊕xn-q.`

Parent topic: Conventions