BlogHide resteemssinbad989 (52)in mathematics • 4 months agoElements of Set Theory: Ordering on Natural NumbersOrdering on Natural Numbers Previously, we have defined natural numbers that was a side effect of our spurious…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: ArithmeticArithmetic We can apply recursion theorem, from the previous section, to define addition and multiplication on .…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: Recursion on Natural NumbersConsider the situation where I want you to guess the function such that I only give you two information; that is…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: Peano's PostulatesHi! I'm Giuseppe Peano, I introduce Peano system to make the life of math students miserable. Source In 1889…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: Inductive SetsIn mathematics, there are two ways of introducing new objects for study, axiomatic approach (e.g. the one we…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: Ordering RelationsElements of Set Theory: Ordering Relations From the first section of this chapter, we've covered about the ordering…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: Equivalence RelationsConsider a set A given by a figure in (a), say we want to partition it into six boxes as in (b). For…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: Infinite Cartesian ProductsWe've encountered in previous section Cartesians products of two sets, this time we will show that we can form…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: FunctionsIn most calculus books a function is introduced as a rule that assigns to each object in a certain set (domain) a…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: n-ARY relationsElements of Set Theory: n-ARY relations You might be wondering why do relations only have to do with ordered pairs.…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: RelationsElements of Set Theory: Relations First let's consider some examples. The ordering relation < on the set is…sinbad989 (52)in mathematics • 4 months agoElements of Set Theory: Ordered PairsElements of Set Theory: Ordered Pairs Consider the following pair set: this can be thought as an unordered…sinbad989 (52)in mathematics • 5 months agoElements of Set Theory: Algebra of SetsElements of Set Theory: Algebra of Sets The two basic operation on sets are operation of union operation…sinbad989 (52)in programming • 5 months agoObject Oriented Programming: Specifying attributes and behaviorsSpecifying attributes and Behaviors We now have now added object-oriented terminology in our arsenal of definitions.…sinbad989 (52)in mathematics • 5 months agoElements of Set Theory: Arbitrary Unions and IntersectionsPreviously, we have the union axiom in its preliminary form, this union operation allowed us to form the union of…sinbad989 (52)in mathematics • 5 months agoElements of Set Theory: AxiomsNow, we are done with the introduction chapter of the book, Elements of Set Theory . Again, I would like to…sinbad989 (52)in mathematics • 5 months agoElements of Set Theory: Historical NotesThe concept of a set is very basic and natural, and has been used in mathematical writings since ancient times. But…sinbad989 (52)in mathematics • 5 months agoElements of Set Theory: NotationElements of Set Theory: Notation To denote sets, we will use a variety of letters, both lowercase (a,b,...)…sinbad989 (52)in mathematics • 5 months agoElements of Set Theory: Axiomatic MethodIn this book, Elements of Set Theory , the axioms of set theory well be stated (in the future sections), and we are…sinbad989 (52)in mathematics • 5 months agoElements of Set Theory: ClassesElements of Set Theory: Classes In accordance with our informal image of the hierarchical way sets are…