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modular:ordered_sets [2014/01/30 00:29] marje |
modular:ordered_sets [2014/01/30 14:21] marje |
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| Of the examples above, sets in 1. are totally ordered, while the set in 3. is not, because, e.g., $2$ and $3$ are incomparable (neither $2 \mid 3$ nor $3 \mid 2$). | Of the examples above, sets in 1. are totally ordered, while the set in 3. is not, because, e.g., $2$ and $3$ are incomparable (neither $2 \mid 3$ nor $3 \mid 2$). | ||
| - | <WRAP indent> | + | <WRAP task> |
| - | :?: Which of the following sets are totally ordered? | + | Which of the following sets are totally ordered? |
| - The set on the Hasse diagram above. ++Answer| No, because, e.g., $\{1\}$ and $\{3\}$ are incomparable.++ | - The set on the Hasse diagram above. ++Answer| No, because, e.g., $\{1\}$ and $\{3\}$ are incomparable.++ | ||
| - The set given by the following ++diagram. | | - The set given by the following ++diagram. | | ||
| Line 65: | Line 65: | ||
| </box> | </box> | ||
| - | <WRAP indent> | + | <WRAP task> |
| - | :?: | + | |
| Exercises on suprema. TODO | Exercises on suprema. TODO | ||
| </WRAP> | </WRAP> | ||
| Line 74: | Line 73: | ||
| </box> | </box> | ||
| - | <WRAP indent> | + | <WRAP task> |
| - | :?: | + | |
| Which of the following sets are lattices? | Which of the following sets are lattices? | ||
| </WRAP> | </WRAP> | ||
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| + | ----------------------------------------------------------------------------------------------------------------------------------------- | ||