Scalar-Output Function

A scalar-output function is a numerical-output function whose function range is a real number interval.

• AKA: Real-Valued Output Function.
• Context:
  • range: Real Numbers.
  • It can range from being a Continuous Real-Valued Function to being a Discontinuous Real-Valued Function.
  • It can range from being a Scalar-Output Vector Function, to being a Scalar-Output Tuple Function, to being a Scalar-Output Numeric Function, to being a Scalar-Output Set Function.
  • It can range from being a Rational-Valued Function to being an Irrational-Valued Function.
  • It can range from being a Scalar-Output Algebraic Function to being a Scalar-Output Function Instance.
• Example(s):
  • an Algebraic Function, such as:
    • a Linear Function, such as [math]\displaystyle{ f(x) = 2.3 x + 6 }[/math].
    • a Polynomial Function, such as [math]\displaystyle{ f(x) = \frac{1}{3} x^2 − 2.3 x + 6 }[/math].
  • [math]\displaystyle{ f(\text{Red}) \rightarrow \pi }[/math].
  • [math]\displaystyle{ f(1.5) ⇒ 5.1 }[/math].
  • [math]\displaystyle{ f(4,Red) \rightarrow \sqrt{2} }[/math].
  • [math]\displaystyle{ f(1.1,\text{Red},3.9)\rightarrow 3.0 }[/math].
  • a Random Variable Function.
  • a Random Scalar Function.
  • …
• Counter-Example(s):
  • a Category-Valued Function, such as [math]\displaystyle{ f(1.1, \text{water}, 3.9) \rightarrow \text{Green} }[/math].
  • an Integer-Valued Function.
  • a Vector-Valued Function, such as [math]\displaystyle{ f(1.1,\text{Red},3.9)\rightarrow (3.4, 1.1) }[/math].
  • a Scalar-Input Function.
  • a Complex-Valued Function.
  • an Imaginary Number-Outcome Function.
  • an Irrational Number-Valued Function.
• See: Mathematical Function Family, Set Operation.

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