Definition of Interval
An Interval is a subset S of a totally
ordered set T with the property that whenever
- x and y are in S and
- z is in T and
- x < z < y
then z is in S.
A "totally ordered" set is a
set over which the £ operator is reflexive,
antisymmetric, transitive, and total...
reflexive: a £ a
antisymmetric: if a £ b and b £
a then a = b
transitive: if a £ b and b £
c then a £ c
total: a £ b or b £
a
The reflexive property restricts the meaning of the £
operator, and the other three properties are satisfied by the real numbers.
Internet References
Source: Wikipedia
Related Pages in this Website
Go back to Calculus Home or visit Calculus
Theorems
Subdividing an Interval
Arithmetic Rules -- properties of
equality, addition, multiplication, and in particular the Axioms of Real
Arithmetic, including the completeness axiom.
Upper Bound -- definition of
"upper bound" and "least upper bound" of either sets or
functions
