Schluessel: 3.18 Ranges of real numbers

3.18 Ranges of real numbers

Procedures for ranges of real numbers.

Reader Syntax: #R[n m]

Reader Syntax: #R(n m]

Reader Syntax: #R[n m)

Reader Syntax: #R(n m)

describes

of real numbers respectively.

Function: make-closed-interval n m

Function: make-left-open-interval n m

Function: make-right-open-interval n m

Function: make-open-interval n m

creates

of real numbers respectively.

Function: neighborhood-of? range obj: returns #t if the object is in the range.

Function: topology-contained? range1 range2: returns #t if range1 is contained in range2.

Function: topology-independent? range1 range2: returns #t if range1 is independent of range2.

Function: topology-empty? range: returns #t if the range is the empty set.

Function: set-maximum range
Function: set-minimum range: gets maximum(minimum) of range, or #f if the range doesn’t have maximum(minimum).

Function: set-supremum range
Function: set-infimum range: gets supremum(infimum) of range, or #f if the range is not bounded.
A range may have supremum(infimum) if the range doesn’t have maximum(minumum).

Function: topology-intersection range …: computes intersection of all given ranges.

Function: topology-closure R
Function: topology-interior R: computes a closure(interior) in sense of set theory.

Function: cardinality->integer cardinality: converts cardinality to an integer. If the cardinality is infinite, this procedure will return #f.

Function: cardinality-finite? cardinality: returns #t if cardinality is finite.

Function: cardinality-countable? cardinality: returns #t if cardinality is countable.

Function: + cardinality …: [R5RS+] adds all given arguments. This procedure extends for cardinality.

Function: * cardinality …: [R5RS+] multiplies all given arguments. This procedure extends for cardinality.

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