A BRIEF HISTORY OF SET THEORY All mathematical topics are mostly emerge and evolve around with many researchers and their theories. However set theory was different. It was founded by one person in a theory in 1874 by Greog Cantor. Set concept was derived from the idea of the infinity. It was started in ancient times where since the 5th century BC, beginning with Greek mathematician Zeno ] and ancient Indian mathematicians had have difficulties in the concept of infinity. there many notable work and progress has been done. The most important is the work of Bernard Bolzano in the first half of the 19th century here where modern understanding of infinity began. In 1867 to1871, with Greog Cantor's work on number theory the infifnity theory was eventually have an understanding. The initial work of Grog Cantor is polarized the mathematician of his time. While Karl Weierstrass and Dedekind supported Cantor and this theory Whereas Leopold Kronecker, now seen as a founder of mathematical constructivism, did no support to Greog Cantor. Later over time This set theory eventually became spread over the place, due to the utility of Cantorian concepts, such as one- to-one correspondence among sets, his proof that there are more real numbers than integers, and the "infinity of infinities" resulting from the power set operation. This utility of set theory led to the article "Mengenlehre" contributed in 1898 by Arthur Schoenflies has validified this set thoery. The next wave of rise in set theory came around 1900, where it was discovered that Cantorian set theory gave rise to several contradictions and arguement among mathematicians it was called and classify as antinomies or paradoxes. Bertrand Russell and Ernst Zermelo independently found the simplest and best known paradox, now called it was named as Russell's paradox. In this paradox it was consider as "the set of all sets that are not members of themselves", which leads to a great contradiction since it must be a member of itself, and not a member of itself. In 1899 Cantor had himself posed the question "What is the cardinal number of the set of all sets?", and obtained a related paradox. Russell used his paradox as a theme in his 1903 review of continental mathematics in his The Principles of Mathematics. And explain more and it validated it parody. The momentum of set theory was such that debate on the paradoxes did not lead to its abandonment. The work of zermelo in 1908 and Abraham Fraenkel in 1922 resulted in the set of axioms ZFC, which became the most commonly used set of axioms for set theory. The work of analysts such as Henri Lebesgue demonstrated the great mathematical utility of set theory, which has since become woven into the fabric of modern mathematics. Set theory is commonly used as a foundational system, although in some areas category theory is thought to be a preferred foundation.
All mathematical topics are mostly emerge and evolve around with
many researchers and their theories. However set theory was
different. It was founded by one person in a theory in 1874 by
Greog Cantor.Set concept was derived from the idea of the infinity.
It was started in ancient times where since the 5th century BC,
beginning withGreekmathematicianZeno ] and ancientIndian
mathematicians had have difficulties in the concept ofinfinity.
there many notable work and progress has been done. The most
important is the work ofBernard Bolzanoin the first half of the
19th century here where modern understanding of infinity began. In
1867 to1871, with Greog Cantor's work on number theory the
infifnity theory was eventually have an understanding.The initial
work of Grog Cantor is polarized the mathematician of his time.
WhileKarl Weierstrassand Dedekind supported Cantor and this theory
Whereas Leopold Kronecker, now seen as a founder ofmathematical
constructivism, did no support to Greog Cantor. Later over time
This set theory eventually became spread over the place, due to the
utility of Cantorian concepts, such asone-to-one
correspondenceamong sets, his proof that there are morereal
numbersthan integers, and the "infinity of infinities" resulting
from thepower setoperation. This utility of set theory led to the
article "Mengenlehre" contributed in 1898 byArthur Schoenflieshas
validified this set thoery.The next wave of rise in set theory came
around 1900, where it was discovered that Cantorian set theory gave
rise to several contradictions and arguement among mathematicians
it was called and classify as antinomiesorparadoxes.Bertrand
RussellandErnst Zermeloindependently found the simplest and best
known paradox, now called it was named asRussell's paradox. In this
paradox it was consider as "the set of all sets that are not
members of themselves", which leads to a great contradiction since
it must be a member of itself, and not a member of itself. In 1899
Cantor had himself posed the question "What is thecardinal numberof
the set of all sets?", and obtained a related paradox. Russell used
his paradox as a theme in his 1903 review of continental
mathematics in hisThe Principles of Mathematics. And explain more
and it validated it parody.The momentum of set theory was such that
debate on the paradoxes did not lead to its abandonment. The work
ofzermelo in 1908 andAbraham Fraenkelin 1922 resulted in the set of
axiomsZFC, which became the most commonly used set of axioms for
set theory. The work ofanalystssuch asHenri Lebesguedemonstrated
the great mathematical utility of set theory, which has since
become woven into the fabric of modern mathematics. Set theory is
commonly used as a foundational system, although in some
areascategory theoryis thought to be a preferred foundation.
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