Sometimes we asked ourself, math? what for? and Some question unanswered. This is my first time learning abstract algebra. only What for remain in my head and its does lead for nothing. Unlike other mathematics branch, we found the useful of math in no time. Say trigonometri, algebra, calculus. But when i got structure class.. blind at all.
Ok, then my advisor tell me. Imagine that you have to be first time human on earth that sent to study outside our solar systems. You met extra terrestrial being. You have to learn their knowledge as an ambassador of mankind. Then you walk into class. You met a new, over new, faces. Even you can't say it faces. Then you start to learn.
Then you heard the teacher say, 'gorifsd'. And all of student answer, 'yuke'. You may not know how exactly what they say, but you could feel or sense that maybe its like our greetings. Then they continue with the class. Teacher say, 'ouri pur koe', while student say, 'tudi'. Next teacher say, 'ouri pur firk', student answer with, 'ikre'. Yeah, you may guess anything, but how bout addition?
Imagine that in that society, 'pur' is a kind of operation. Then 'ouri, koe, firk, tudi, ikre,' is somewhat as number than relate each other especially by operation 'pur'. Yeah, it can be anything. But thinking like that helpful for some degree i though. Then we can general our knowledge of operation and sets. We think that 1 + 2 always equal to 3. But, if we define '+' and '=' on other way, so far that we could not predict what happen to our number, what is rules, or other building of knowledge that keep it consistent?
When you studying structure, we will find a new world and new point of view. When it make sense, we will know that our knowledge is a gift for living. Also we could be wise. The other, its build math consistent and applicable on any given condition, even it doesn't mean math could satisfy any condition. For starting, you should try to read "Alice adventure in wonderland". Its a good movie and full of logical term.
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