Math WS 1 Vocab Quiz

A set containing all real numbers between endpoint1 and endpoint2. The endpoints can be real or infinite (either –∞, or ∞). If the ____ is not the empty set, then endpoint1 is not greater than endpoint2.

• Open interval

• Degenerate interval

• Real interval

• Proper interval

The function f: X →Y, is invertible iff there exists a function, h: Y →X such that h⸰f = id X and f⸰h = id Y. Alternative definition: the function f: X →Y, is invertible iff there exists a function, h: Y →X such that ∀x ∈ X, y=f(x), when x=h(y).

• Invertible Function

• Inverse Function

• Partial Function

• Involuntary Function

A real interval containing no real numbers between endpoint1 and endpoint2, where the endpoints are real and equal. Any interval with endpoint1 > endpoint2 is also considered empty.

• Zero interval

• Degenerate interval

• Real interval

• Empty interval

A function, ι: X →Y, which always produces a value equal to its argument and X is a subset of Y

• Identity Function

• Inverse Function

• Partial Function

• Inclusion Function

A real interval, for which there exists no real number smaller than all elements in the interval and no real number larger than all elements in the interval. Alternative definition – a real interval that is left-unbounded and right unbounded.

• Unbounded interval

• Closed interval

• Infinite interval

• Proper interval

A function, id X : X →X, which always produces a value equal to its argument

• Identity Function

• Inverse Function

• Partial Function

• Inclusion Function

A real interval, which is neither empty nor degenerate. Alternative definition – a real interval is proper iff it contains uncountable many real numbers.

• Open interval

• Degenerate interval

• Real interval

• Proper interval

A set containing only one real number between endpoint1 and endpoint2, where the endpoints are real and equal

• Open interval

• Degenerate interval

• Real interval

• Proper interval

function, f: X →X, that is its own inverse. Alternative definition – a function, f: X →X, is involutory if f⸰f = id X.

• Invertible Function

• Inverse Function

• Partial Function

• Involuntary Function

A real interval, for which there exists one real number smaller than all elements in the interval and there exists another real number larger than all elements in the interval. Alternative definition – a real interval that is left-bounded and right-bounded.

• Bounded interval

• Degenerate interval

• Closed interval

• Proper interval