Cantor

famous German mathematician, Georg Cantor is known for discovering and building a hierarchy of infinite sets according to their cardinal numbers. He is also known for inventing the Cantor set, which is now a fundamental theory in mathematics. Georg Ferdinand Ludwig Philipp Cantor was born on March 3, 1845 in Saint Petersburg, Russia, to Georg Waldemar Cantor and Maria Anna Bohm. His father was a German Protestant and his mother was Russian Roman Catholic. Cantor was brought up as a staunch Protestant

Georg Ferdinand Ludwig Philipp Cantor was born on March 3, 1845 in Saint Petersburg, Russia. His father, Georg Waldemar Cantor, was a successful merchant working as a wholesaling agent, then later found another job as a broker in the St. Petersburg Stock Exchange. Georg’s father was born in Denmark and had a deep passion for culture and arts. His mother, Maria Anna Böhm, was from Russia and very musical. Georg inherited his love for music and arts from his parents, considering he was a wonderful

Georg Cantor I. Georg Cantor Georg Cantor founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series and was the first to prove the nondenumerability of the real numbers. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg, Russia, on March 3, 1845. His family stayed in Russia for eleven years until the father's sickly health forced them to move to the more acceptable environment of Frankfurt

2014 House Majority leader Eric Cantor would lose his bid for re-election to a relatively underwhelming opponent Dave Brat a Tea Party-backed economics professor. This primary “upset” (Martin, June 2014) is considered one of the biggest upsets in political history. Cantor who had raised roughly 5.4 million dollars in campaign funds found himself down by eleven percent to Brat who had only been able to raise roughly two hundred thousand for his own campaign. While Cantor continuously criticized Brat

we had a set of all prime numbers, the number 4 could not belong to the set as it has more positive divisors than just 1 and itself -- it violates the specific criteria for membership in the set. There are two types of sets as defined by Georg Cantor: finite and infinite. A finite set is simply one whose size, or cardinality, can be defined by a natural number. Cardinality describes the number of elements contained in a set. The members of any set (finite or infinite) can be placed in a

Finiteness has to do with the existence of boundaries. Intuitively, we feel that where there is a separation, a border, a threshold – there is bound to be at least one thing finite out of a minimum of two. This, of course, is not true. Two infinite things can share a boundary. Infinity does not imply symmetry, let alone isotropy. An entity can be infinite to its “left” – and bounded on its right. Moreover, finiteness can exist where no boundaries can. Take a sphere: it is finite, yet we can continue

A Discussion on the History, Variations, and Applications of Infinity Infinity is perhaps one of the most frequently encountered idea in today’s world. This concept of endlessness is what people normally associate with when discussing infinity, and it has become something that we have integrated into everyday language. Although it may seem to be simple concept, infinity is actually a widely debated and argued topic, and it has shown to be more complex than it initially appears to be. There are

Aristotle supported the idea of “potential infinity” but refuted the idea of “actual infinity”. He defined potential infinity by saying if you are counting natural numbers, logic would tell us that we can always add one to the previous number and that can potentially go on forever. He also said that we could potentially use this logic in geometry if we imagined a line that extended beyond both points with no recognizable end. On the contrary, actual infinity seems paradoxical because even if we had

theory is an area of mathematics that deals with inconceivable numbers, and bottomless concepts such as infinity. The history of set theory is relatively dissimilar from the history of most other parts of mathematics. Set Theory was founded by Georg Cantor in 1874 in his paper “On a Characteristics Property of All Real Algebraic Numbers”. Naive set theory is fun, and as we saw with Cantor’s diagonalization, it can produce some incredibly beautiful results. But as we’ve seen before, in the simple world

infinity. However, they did not actuaily delve into the entirety of this number. The Greeks used the term “potentially infinite," for the concept of an actual limitless value was beyond their comprehension. The actual term “infinity” was defined by Georg Cantor, a renowned German mathematician, in the late nineteenth century. It was originally used in his Set Theory, which is a very important theory to the mathematical world. The value of infinity can get a bit confusing, as there are different types of