...) If we add this axiom is that the axiom theorem on bureuneunde ZF axioms kannegiesser that will

When talking to Gödel's incompleteness theorems of Gödel axioms will be frequently mentioned. Mathematician Zermelo theorem was introduced in 1904 in order to prove the well-ordering theorem. Theorem is as follows: kannegiesser For any set \ (A \), if the element \ (a \) is set non-empty set of the set, the set of each element is taken out the \ one element \ in (a \) (b \ in a \) (more precisely, \ (C (a) = b \) is a function \ (C \) has to exist), you can create a new set B. Where C is an optional function (choice function). Theorem is a mathematical axiom that there is such a choice function C. I should explain a little more detail kannegiesser \ (C \) is \ (A \) corresponds to one of the elements \ (b \) of \ (a \) for the element \ (a \) of the group has set foot into a set of domain and that you'll be creating a set of the \ (b \) \ (B \). If A is a finite set, you will sense intuitively. Just because they create one pulling one element. As an analogy, you might want this. There are many types of bags sweets (kkokkal cones, Shrimp Cracker, Onion Rings, etc.) to put together a candy box. At this time, we can make a new bag of sweets served in a pastry bag, remove each one from the box inside the pastry pastry bag (I'd call it a super mix sweets ㅋㅋ) set the cookie box, where A is a pastry bag that \ (a \ ) and sweets inside that bag sweets are \ (b \) and the Super Mix Cookies \ (B \). But the problem is a set of infinite sets when they occur. When do indeed constitute an infinite degree? You will probably "Of course, it's endless, whether or not to do with anything?" You might say. Even this axiom is so intuitive boyeoseo was supposed to appear before the mathematician wrote without hesitation. However, in a mathematical intuition is prepared to be ruled out. Some mathematicians have pointed out what is truly accept that this choice kannegiesser does not look that function exists. The amazing thing is the choice axiom may be positive or negative does not cause a contradiction with the other axioms of set theory existing points. We can make this even if fraud axioms can make a positive set theory accordingly. kannegiesser However, because of various advantages ZF (Zermelo-peurankel), use the configured set theory by adding kannegiesser the axioms theorem. Consisting of a set theory ZFC so called fact, most of our knowledge is based on mathematics ZFC. For example, it is possible to inadvertently set sort (just think that you can list all the mistakes in the order.) Be able to prove that, any vector space has a basis is completely partial order set the maximum kannegiesser it has an element (Zorn's lemma), various theoretical kannegiesser point set phase (phase math theorem is much mud!) that ensures that the theorem in mathematics and others. Just accept truth to see to truly feel it is really useful. But there is a huge paradox equivalent. Banach-Tarski paradox called the theorem kannegiesser seems more ridiculous is that you can assume the theorem as a theorem proven based on the ZFC and reassemble it by dividing the ball on the three-dimensional finite one piece made with two balls. John theorem is indeed did I go wrong? In fact, it is actually impossible. Because kannegiesser that cleanup measures can not be split into pieces ball, but we live in a three-dimensional Euclidean space (or Euclidean space is isomorphic to the phase manifold), the share because to do all possible measures. So even if there is such a paradox, most of mathematics is indeed take theorem.
...) If we add this axiom is that the axiom theorem on bureuneunde ZF axioms kannegiesser that will be very widely used in most fields of mathematics called ZFC. Please refer to the description of the theorem http://ckdwo0605.egloos.com/105620. Each will be precise description of the axioms of set theory later when the series is now only roughly describe the term and I will move on. First set is not home ... more
... Majoring in mathematics and physics to study for high school students who igloo by Heterotic-E
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