Definition:Termial/Real Numbers

Definition

Let $x \in \R$ be a real number.

The termial of $x$ is denoted $x?$ and defined as:

$x? = \dfrac {x \paren {x + 1} } 2$

Also see

• Closed Form for Triangular Numbers

Historical Note

The termial was invented by Donald E. Knuth in his The Art of Computer Programming.

It was devised as an analogy of the factorial, so as to illustrate the extension of the latter to the real numbers.

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.5$: Permutations and Factorials: $(9)$