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OpenMath Content Dictionary: interval1

Canonical URL:
http://www.openmath.org/cd/interval1.ocd
CD Base:
http://www.openmath.org/cd
CD File:
interval1.ocd
CD as XML Encoded OpenMath:
interval1.omcd
Defines:
integer_interval, interval, interval_cc, interval_co, interval_oc, interval_oo, oriented_interval
Date:
2009-04-01
Version:
4
Review Date:
2014-04-01
Status:
official


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     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

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          work to the original source.
       b) The fact that the derived work is not the original OpenMath 
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          both this document and the derived work are Content Dictionaries
          then the derived work must include a different CDName element,
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This CD holds symbols which describe both discrete and continuous 1-dimensional intervals (with open/closed end points). There is also an oriented_interval, for use in integration


integer_interval

Role:
application
Description:

A symbol to denote a discrete 1 dimensional interval from the first argument to the second (inclusive), where the discretisation occurs at unit intervals. The arguments are the start and the end points of the interval in that order.

Example:
The integer interval 1, 2, ..., 10.
[ 1 , 10 ]
Formal Mathematical property (FMP):
n [ a , b ] ( n Z le ( a , n ) le ( n , b ) )
Signatures:
sts


[Next: interval] [Last: interval_co] [Top]

interval

Role:
application
Description:

A symbol to denote a continuous 1-dimensional interval without any information about the character of the end points (used in definite integration). The arguments are the start and the end points of the interval in that order.

Example:
The interval 1.0, ..., 10.0.
( 1.0 , 10.0 )
Formal Mathematical property (FMP):
( a , b ) [ a , b ]
Formal Mathematical property (FMP):
( a , b ) ( a , b )
Signatures:
sts


[Next: oriented_interval] [Previous: integer_interval] [Top]

oriented_interval

Role:
application
Description:

A symbol to denote a continuous 1-dimensional interval without any information about the character of the end points (used in definite integration). The arguments are the start and the end points of the integration, in either order.

Example:
defintint ( oriented_interval ( a , b ) , f ) = defintint ( oriented_interval ( b , a ) , f )
Signatures:
sts


[Next: interval_oo] [Previous: interval] [Top]

interval_oo

Role:
application
Description:

A symbol to denote a continuous 1-dimensional interval with both end points excluded from the interval. The arguments are the start and the end points of the interval in that order.

Example:
The continuous open interval (1,10).
( 1 , 10 )
Formal Mathematical property (FMP):
x ( a , b ) ( x R a < x x < b )
Signatures:
sts


[Next: interval_cc] [Previous: oriented_interval] [Top]

interval_cc

Role:
application
Description:

A symbol to denote a continuous 1-dimensional interval with both end points included in the interval. The arguments are the start and the end points of the interval in that order.

Example:
The continuous closed interval [1,10].
[ 1 , 10 ]
Formal Mathematical property (FMP):
x [ a , b ] ( x R le ( a , x ) le ( x , b ) )
Signatures:
sts


[Next: interval_oc] [Previous: interval_oo] [Top]

interval_oc

Role:
application
Description:

A symbol to denote a continuous 1-dimensional interval with the first point excluded from the interval, but the last included. The arguments are the start and the end points of the interval in that order.

Example:
The continuous interval open at the lower bound and closed at the higher bound (1,10].
( 1 , 10 ]
Formal Mathematical property (FMP):
x ( a , b ] ( x R a < x le ( x , b ) )
Signatures:
sts


[Next: interval_co] [Previous: interval_cc] [Top]

interval_co

Role:
application
Description:

A symbol to denote a continuous 1-dimensional interval with the first point included in the interval, but the last excluded. The arguments are the start and the end points of the interval in that order.

Example:
The continuous interval closed at the lower bound and open at the higher bound [1,10).
[ 1 , 10 )
Formal Mathematical property (FMP):
x [ a , b ) ( x R le ( a , x ) x < b )
Signatures:
sts


[First: integer_interval] [Previous: interval_oc] [Top]

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