**Random/Randomness**
Without cause; not compressible; obeying the statistics of a fair
coin toss.

**Random Walk**
A walk in one or more dimensions that is dictated by the outcome of a
coin toss. The direction of each step of the walk is specified by the
coin toss. The resulting random motion is often referred to as
Brownian motion.

**Rational Number**
A number that can be expressed as a fraction.

**Real Number**
Any number that can be represented with a potentially infinite decimal
expansion to the right of the decimal point. Natural,
rational, irrational, and incomputable numbers are all
real numbers.

**Recurrent Neural Network**
A network similar to a feedforward neural network except that
there may be connections from an output or hidden layer to the
inputs. Recurrent neural networks are capable of universal
computation.

**Recursive**
Strictly speaking, a set or function is recursive if it is
computable; however, in the usual sense of the word, a
function is said to be recursive if its definition make reference
to itself. For example, factorial can be defined as x! = x * (x -
1)! with the base case of 1! equal to 1. See also
self-referential.

**Recursively Enumerable (RE)**
A potentially infinite set whose members can be enumerated by a
universal computer; however, a universal computer may not be able
to determine that something is not a member of a recursively
enumerable set. The halting set is recursively enumerable but
not recursive.

**Reductionism**
The idea that nature can be understood by dissection. In other words,
knowing the lowest-level details of how things work (at, say, the
level of subatomic physics) reveals how higher-level phenomena come
about. This is a bottom-up way of looking at the universe, and
is the exact opposite of holism.

**Regular Expression**
A definition for a class of strings that can be recognized by a
finite-state automaton. An example of a class of strings that is
regular would be legal mathematical expressions using only ``+'' and
digits. An example that is not regular is the same legal
mathematical expressions as before, but with properly nested
parentheses.