There is no need to check the left child after this final step : at the start, the max-heap was valid, meaning 11 > 5; if 15 > 11, and 11 > 5, then 15 > 5, because of the transitive relation.
22.
Examples of transitive relations include the equality relation on any set, the " less than or equal " relation on any linearly ordered set, and the relation " " x " was born before " y " " on the set of all people.
23.
It cannot be identified with both B and C, for identity is a transitive relation, and B is certainly not the same amoeba as C . Yet, the fission was symmetrical, so neither B nor C has any more or less claim to be A than the other.
24.
To show that the above definition of " R " + is the least transitive relation containing " R ", we show that it contains " R ", that it is transitive, and that it is the smallest set with both of those characteristics.
25.
His work, " A Treatise on Book Titles ", he writes on existence, and how time and place are associated with existence . al-Amidi also wrote about linguistics . " On Substantiation Through Transitive Relations " discusses figurative speech in the first two sections.
26.
This is obtained by first adding the pair " xRy " to the relation, which may result in a non-transitive relation, and then restoring transitivity by adding and all pairs " qRp " such that " qRx " and " yRp ".
27.
Formally, the issue is that " interfertility " ( ability to interbreed ) is not a transitive relation if A can breed with B, and B can breed with C, it does not follow that A can breed with C and thus does not define an equivalence relation.
28.
:: While that's what guidelines may say, " is a " cases are transitive relations and these situations should be considered trivial to prove ( even if without a secondary source explicitly noting that poodles are mammals ) . talk ) 16 : 31, 22 June 2009 ( UTC)
29.
Therefore, it is guaranteed ( 1 ) that the above definition of " " better " " really defines a transitive relation and ( 2 ) that there is always at least one candidate D with p [ D, E ] \ ge p [ E, D ] for every other candidate E.
30.
Around the same time that George Boole was developing his system of algebra ( 1847 ) so important to computer science Augustus de Morgan was finalising his own logic of relations in a paper entitled " Formal Logic " published in 1849 . The syllogisms of subject-predicate logic were to be replaced in his system by what he was to call transitive relations.
