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Partial OrdersEdit

Part AEdit

One example of a partial order that is not a total order is comparing the hitting ability of different baseball players. Say that we compare these players by number of homeruns hit, RBI's, and batting average where player $A\preccurlyeq B$ if and only if $A$'s homeruns hit, RBI's, and the batting average is less than or equal to each of $B$'s. This ordering is reflexive because for any player $A$ there homeruns, RBI's, and batting average is equal to itself. This ordering is antisymmetric because it is impossible for two players $A$ and $B$ to have the same batting average and not be the same player.

Part BEdit

3Edit

Proof Wiki DefinitionsEdit

Eulerian Graph
Characteristics of Eulerian Graph

AEdit

Related ArticlesEdit

Partial Order

4Edit

AEdit

First we place the L. We have 7 places to choose. Next we pick a vowel out of 5 and select a location out of 6 places. Next we pick a vowel out of 5 and pick a location for it out of 5 places. Pick one digit out of ten and a location for it out of the four remaining. Pick one digit out of ten and a location for it out of the three remaining. Pick one digit out of ten and a location for it out of the two remaining. Pick a letter that is not a vowel and put this letter in the last location.

By the multiplication rule we arrive at \[(1\cdot 7) \cdot (5 \cdot 6) \cdot (5 \cdot 5) \cdot (10 \cdot 4) \cdot (10 \cdot 3) \cdot (10 \cdot 2) \cdot (21 \cdot 1) = 2,646,000,000. \]

BEdit

Pick a location out of seven for the first 7. Next pick a location out of six for the second 7. Next we pick from the group of letters and digits excluding the five vowels and the five even digits. We choose a spot for this out of the five remaining. We continue to do this the the last four spots.

By the multiplication rule we arrive at \[ (1 \cdot 7) \cdot (1 \cdot 6) \cdot (26 \cdot 5) \cdot (26 \cdot 4) \cdot (26 \cdot 3) \cdot (26 \cdot 2) \cdot (26 \cdot 1) = 59,882,135,040. \]

CEdit

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