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5. (1) Show that the lexicographical order on {0, 1}x N with the standard orders on {0, 1} and on N is a well order. (2) Let w be the ordinal of N with the standard order (called the first limit ordinal). The example above has ordinal w+w by the definition of the sum of ordinals. Show that ww+w.

5. (1) Show that the lexicographical order on {0, 1}x N with the standard orders on {0, 1} and on N is a well order. (2) Let w be the ordinal of N with the standard order (called the first limit ordinal). The example above has ordinal w+w by the definition of the sum of ordinals. Show that ww+w.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. (1) Show that the lexicographical order on {0, 1} × N with the standard orders on {0, 1} and on N is a well order. (2) Let w be the ordinal of N with the standard order (called the first limit ordinal). The example above has ordinal w+w by the definition of the sum of ordinals. Show that ww+w.
Transcribed Image Text:5. (1) Show that the lexicographical order on {0, 1} × N with the standard orders on {0, 1} and on N is a well order. (2) Let w be the ordinal of N with the standard order (called the first limit ordinal). The example above has ordinal w+w by the definition of the sum of ordinals. Show that ww+w.
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