Brief introduction of Cantor's life
Cantor is a famous mathematician in the world. He was born in 1845 and died in 19 18. He is the founder of set theory and super-finite number theory. His achievements have changed the trend of people studying mathematics in the world and solved the problems that mathematicians have been difficult to solve for a long time. Let's take a look at Cantor's profile:
Cantor is a German mathematician, but his birthplace is not in Germany, because he was born in Leningrad, Russia, which is now St. Petersburg, Russia. He is Jewish, his father is a Jewish Danish businessman except evil, and his mother comes from a noble family. She comes from an artistic family.
Cantor's academic performance was excellent, so he entered the famous Berlin University to study mathematics and theology. His tutors include kummer, Wilstrass and Kroneck, all of whom were very famous figures at that time and had high academic achievements.
From Cantor's brief introduction, we know that Cantor's interest in early mathematics is not his greatest achievement, but number theory. Later, Cantor was directly influenced by Wilstrass, so his research direction began to change, from number theory to strict analytical theory. Because of his outstanding talent and unique way of thinking, he quickly emerged.
In later research, Cantor went further, summed up his own research, and finally formed his own mathematical theory. This is the greatest mathematical achievement at that time, because he summed up the theory of set theory and super-finite number, which caused great repercussions in the mathematical and theological circles at that time.
However, Cantor's mathematical theory was opposed and attacked by people at that time, which once led to his mental disorder. Although he got better after treatment, he was always troubled by the disease and eventually died.
Cantor's achievements.
Cantor is a famous German mathematician, and his contribution to mathematics is unparalleled. Cantor's achievements are set theory and super-finite number theory. These two theories became the most important mathematical theories in the world at that time, which provided guidance for many mathematicians at that time and promoted the development of the whole mathematics.
One of Cantor's achievements is set theory. Cantor found something different in the research of finding the uniqueness criterion of function expansion into trigonometric series. After his long-term research, he finally realized the importance of infinite set and began to study the theory of infinite set.
In order to extend the concept of the number of elements in a finite set to an infinite set, Cantor began to use the principle of one-to-one correspondence, and finally put forward the concept of advanced set equivalence. This is the original version of his set theory. Later, after years of painstaking research and new theories, he formed his own set theory.
Another achievement of Cantor is the theory of super-finite numbers. This is a complicated concept. He has several principles. One is * * * and the other is three generating principles. By repeatedly applying these three principles, we can get the sequence of super-poor numbers, and finally we can deduce the theory of super-poor numbers. These two achievements are all Cantor's mathematical achievements, but because of his avant-garde, they were unanimously opposed by mathematicians at that time.
Cantor's two theories had a great shock in mathematics and theology at that time. People don't want to believe his research, and there are some loopholes in his research, so she is always attacked and even suffers from mental illness. But now it seems that his research is extremely remarkable, and he is a great man who changed the mathematical world.
Cantor paradox
Cantor is a world-famous mathematician, and almost all the mathematical revolutions in the 20th century were completed by him alone. Scientific research will always encounter obstacles. Cantor's paradox is a great contribution to mathematics, but this theory also encountered great obstacles at that time.
There are two main points in Cantor's theory, one is the set theory, the other is the super-finite number theory; These two points are also famous in the field of mathematics today. In Cantor's research, one-to-one method research has caused the paradox in infinity, which is Cantor's paradox. Because it is incompatible with traditional ideas, it was seriously hostile when it was first put forward, and some even thought that Cantor was a madman.
Up to now, Cantor's paradox we have seen is correct and a contribution to mathematics, but the obstacles he encountered when he put it forward at that time were unimaginable. The biggest blow to his theory was his former teacher Kroneck. Kroneck used to be Cantor's teacher, but his students' research surpassed him, so he gave Cantor a merciless blow, out of jealousy.
At the same time, Kroneck also tried to block Cantor's promotion. He was already a professor of great status, so he was deprived of his position at the University of Berlin in order to prevent the development of Cantor.
After the formation of Cantor's paradox, Cantor fell into the whirlpool of long-term debate. Due to long-term fatigue and fierce debate, Cantor was overwhelmed and had a mental breakdown at 1884. Later, after treatment, his theory was supported by many people in a few years, and Cantor's theory was carried forward.
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