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Computer Arithmetic and Validity
book

Computer Arithmetic and Validity

by Ulrich Kulisch
April 2013
Intermediate to advanced content levelIntermediate to advanced
456 pages
16h 7m
English
De Gruyter
Content preview from Computer Arithmetic and Validity
Section 4.1 Interval sets and arithmetic 93
(c) If fR, N , C, , =, g is an ordered division ringoid, then fIR,
e
N ,
+
,
,
/
,
g with
e
N :DfA 2 IR j A \ N ¤ ¿g is also an ordered division ringoid.
Moreover, for all A D Œa
1
, a
2
2 IR and B D Œb
1
, b
2
2 IR n
e
N we have
(E) A 0 ^ 0 <b
1
b
2
) A
/
B D Œa
1
=b
2
, a
2
=b
1
,
(F) A 0 ^ b
1
b
2
< 0 ) A
/
B D Œa
2
=b
2
, a
1
=b
1
,
(G) A 0 ^ 0 <b
1
b
2
) A
/
B D Œa
1
=b
1
, a
2
=b
2
,
(H) A 0 ^ b
1
b
2
< 0 ) A
/
B D Œa
2
=b
1
, a
1
=b
2
.
Proof. (a) Theorem 3.5 directly implies the properties (D1, 2, 3, 4, 5, 7, 8, 9) and (OD5).
It remains to show (A), (D6), (OD1), and (OD2). Let be A D Œa
1
, a
2
, B D Œb
1
, b
2
,
C D Œc
1
, c
2
.
(A): We demonstrate the
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Publisher Resources

ISBN: 9783110301731