Pre-preparation
Background and needs
The purpose of this task is to construct a set of triggers for a relational extraction model. Simply put, it tells the model which triggers correspond to which relationships.
Dataset
...About 8 min
9:1
And God blessed Noah and his sons, and said unto them, Be fruitful, and multiply, and replenish the earth.
众神赐福给Noah和他的儿子，对他们说，你们要生养众多，遍布大地。
...About 4 min
8:1
And God remembered Noah, and every living thing, and all the cattle that was with him in the ark: and God made a wind to pass over the earth, and the waters asswaged;
神纪念Noah和方舟里的一切走兽牲畜。神叫风吹地，水势渐落。
...About 5 min
7:1
And the LORD said unto Noah, Come thou and all thy house into the ark; for thee have I seen righteous before me in this generation.
耶和华对Noah说，你和你的全家都要进入方舟，因为在这世代中，我见你在我面前是义人。
...About 4 min
6:1
And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them,
当世上的人多起来，并生女儿的时候，
...About 6 min
5:1
This is the book of the generations of Adam. In the day that God created man, in the likeness of God made he him;
这里开始是Adam的后代记载的。神造人的日子，是按照自己的样式造的。
...About 4 min
Overview
Given the equivalence relation on A set , we can divide into several equivalence classes by . These equivalence classes form a partition of a set.
Conversely, given a partition of a set, we can define an equivalence relation: if two elements belong to the same subset, then they are equivalent. This gives us an equivalence relation.
...About 3 min
Theorem
Let be a group, any subgroup of , then the number of left (right) cosets of in is called the index of in , denoted as .
Lagrange's Theorem：
is a finite group, any subgroup of , then .
Proof: Let , then there are distinct left cosets of , denote , then is a partition of (Partition is not covering, cosets in are not overlapped), at this time we have
...About 2 min
Definition
Let be a subgroup of (i.e., ). If for all , , then is called a normal subgroup of (or an invariant subgroup), denoted as .
In this case, the left and right cosets are simply called cosets.
The two trivial subgroups of , and itself, are normal subgroups.
...About 2 min
Overview
Review the definition of symmetry group:
Let be an arbitrary set. . The group formed by the composition of such permutations is called the symmetric group on . -
Why is it called a symmetric group? This is because such groups describe the symmetry of objects. - In nature and real life, many objects have symmetry, such as isosceles triangles, squares, and regular polyhedra in geometric shapes. The symmetry of these shapes can be described as a transformation in the plane or space where the image of the shape coincides with itself.
...About 5 min