Sequence Concatenation

A Sequence Concatenation is an Associative Operation that joins two or more sequences.

• Example(s):
  • String Concatenation,
  • Numbers Concatenation,
  • Matrix Concatenation,
  • Vector Concatenation.
  • …
• Counter-Example(s):
  • Append Operation,
  • Splitting Operation.
• See: Programming Language Operator, Programming Language Function.

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References

2021a

• (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Concatenation Retrieved:2021-2-21.
  • In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenation theory, also called string theory, string concatenation is a primitive notion.

2021b

• (Wolfram MathWorld) ⇒ https://mathworld.wolfram.com/Concatenation.html Retrieved:2021-2-21.
  • QUOTE: The concatenation of two strings $a$ and $b$ is the string $ab$ formed by joining $a$ and $b$. Thus the concatenation of the strings "book" and "case" is the string "bookcase". The concatenation of two strings $a$ and $b$ is often denoted $ab$, $a\parallel b$, or, in the Wolfram Language, $a<>b$. Concatenation is an associative operation, so that the concatenation of three or more strings, for example abc, abcd, etc., is well-defined.

The concatenation of two or more numbers is the number formed by concatenating their numerals. For example, the concatenation of $1,234$, and $5678$ is $12345678$. The value of the result depends on the numeric base, which is typically understood from context.

The formula for the concatenation of numbers $p$ and $q$ in base $b$ is

$p\parallel q=pb^{l(q)}+q$,

where

$l(q)=\left\lfloor\log _{b} q\right\rfloor+1$

is the number length of $q$ in $base$ $b$ and $\lfloor x\rfloor$ is the floor function.

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