Equivalence relation and research object of abstract algebra

1. Abstract algebra is more abstract than that. Of course, as engineering students, our specialty is to use the more tangible things to help understand.

First, the object of abstract algebra is primarily a collection, and this set defines some operations (subtraction and the like).

2. Then talk about relationships. You see here, you think, relationship? So EZ. Because we are all intelligent, so the relationship is really as we think, very complex, and many. Simply said, greater than, less than, unequal so relations. What I'm talking about is a mathematical relationship. Ha, not seven aunt eight, but it can be an analogy to help understand is also no harm.

3. Since the relationship is so "many", how do mathematicians study it? To bring all the relationships to the study, obviously not, why? Because many relationships do not have a more comfortable nature, the study does not use, this does not waste precious spirit and youth? (Mathematicians are geniuses, time wasted is not the ordinary people so unworthy of money!) ）。 So research is going to be a good "relationship". This is like our people and people will say to spend more time with friends Ah, family Ah, is a truth, research we feel more important relationship.

4. So there is the argument that there is a equivalence relationship. What? What is an equivalence relationship? First of all, the definition of Kazakhstan, A and b are recorded as a R b; if the relationship is an equivalence relationship, then three conditions must be met:

(1) Reflexivity: a R A

(2) Symmetry: a R B, b r A

(3) transitivity: a R B, b r C can get a r c

So complicated?? Then how can you remember to live? is a drop, the mathematical expression is so rigorous (verbose). So as a science student, how to turn these things into something that you can understand, you can quickly remember AH.

5.how to understand?

(1) First of all, reflexivity is the relationship between oneself and oneself. Well, think about the relationship between yourself and yourself. You don't recognize yourself? I dare not say that I am that way. (such as admitting oneself is a criminal), joke, this kind of relationship how can we study, after all, to carry forward the social positive energy!!! Well, the positive energy of the things we will go to study, of course, also told me to admit themselves, accept themselves. (pulled away).

(2) Symmetry: I have a relationship with you, but you say you and I do not matter, this .... What about the equivalence relationship? I have you, you have me, you do not admit that I have a relationship, could there be you out of someone? (Remember when the confession, said we will be a family later)

(3) Transitivity: This good understanding ah, since the relationship above is so "positive energy", nature is to advertise it, is so called, a friend more road good go.

6. Summary:

Say so much, equivalence relationship with "best friend, girlfriends, brothers, most love you people." "Such words can be word. I and myself must be the best friend, as the saying goes, the person who knows himself best is himself. (reflexive), between friends that must be mutual recognition well (symmetry), friend of friends that is friends ah (think of Liangshan 108 will not), to do big things son, must establish this equivalence relationship, otherwise how to pull up the team. So the abstract algebra is to define the equivalence relationship, well, to do the rhythm of major events.

Later think of the equivalence relationship, that nature is congenial, Gandanxiangzhao synonymous.

Do you remember? (Abstract algebra remember can chew)

Equivalence relation and research object of abstract algebra