Numbers Concatenation

A Numbers Concatenation is a Sequence Concatenation that joins the numerals of two or more numbers.

• Context:
  • It can be mathematically defined $p\parallel q=pb^{l(q)}+q$ where both $p$ and $q$ are both numbers, $l(q)=\left\lfloor\log _{b} q\right\rfloor+1$ is the number length of $q$ in base $b$, $\lfloor \cdot\rfloor$ is the floor function.
• Example(s):
  • $1,234$ and $5678$ can be concatenated into a single number $12345678$
• Counter-Example(s):
  • String Concatenation,
  • Append Operation,
  • Matrix Concatenation,
  • Splitting Operation.
• See: Primitive Notion, Formal Language, Computer Programming, Character String (Computer Science), Wikt:End-to-End, Concatenation Theory.

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References

2021b

• (Wolfram MathWorld) ⇒ https://mathworld.wolfram.com/Concatenation.html Retrieved:2021-2-21.
  • QUOTE: 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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