sinbad989(25)•in #drugwars-fight•2485 days agoCheck my latest fight ! ophro vs sinbad989...2sinbad989(25)•in drugwars-fight•2485 days agoCheck my latest fight ! ophro vs sinbad989...2
sinbad989(25)•in #mathematics•2752 days 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 definition, e.g. . Also, we have the following si...10sinbad989(25)•in mathematics•2752 days 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 definition, e.g. . Also, we have the following si...10
sinbad989(25)•in #mathematics•2760 days agoElements of Set Theory: ArithmeticArithmetic We can apply recursion theorem, from the previous section, to define addition and multiplication on . Suppose we want a function such that is the res...1sinbad989(25)•in mathematics•2760 days agoElements of Set Theory: ArithmeticArithmetic We can apply recursion theorem, from the previous section, to define addition and multiplication on . Suppose we want a function such that is the res...1
sinbad989(25)•in #mathematics•2765 days 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, 1. a starting value 2. a function such that fo...5sinbad989(25)•in mathematics•2765 days 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, 1. a starting value 2. a function such that fo...5
sinbad989(25)•in #mathematics•2767 days 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, Peano published a study giving an axiomatic approa...7sinbad989(25)•in mathematics•2767 days 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, Peano published a study giving an axiomatic approa...7
sinbad989(25)•in #mathematics•2768 days agoElements of Set Theory: Inductive SetsIn mathematics, there are two ways of introducing new objects for study, 1. axiomatic approach (e.g. the one we have used for sets) The concept of set is one of...0sinbad989(25)•in mathematics•2768 days agoElements of Set Theory: Inductive SetsIn mathematics, there are two ways of introducing new objects for study, 1. axiomatic approach (e.g. the one we have used for sets) The concept of set is one of...0
sinbad989(25)•in #mathematics•2770 days agoElements of Set Theory: Ordering RelationsElements of Set Theory: Ordering Relations From the first section of this chapter, we've covered about the ordering relation of the ordered set Now we want to c...1sinbad989(25)•in mathematics•2770 days agoElements of Set Theory: Ordering RelationsElements of Set Theory: Ordering Relations From the first section of this chapter, we've covered about the ordering relation of the ordered set Now we want to c...1
sinbad989(25)•in #mathematics•2771 days 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 example, take, we can partition into six parts: By partitio...1sinbad989(25)•in mathematics•2771 days 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 example, take, we can partition into six parts: By partitio...1
sinbad989(25)•in #mathematics•2773 days 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 something like the Cartesian product but of infin...0sinbad989(25)•in mathematics•2773 days 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 something like the Cartesian product but of infin...0
sinbad989(25)•in #mathematics•2773 days 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 unique object in a possibly different set (ran...2sinbad989(25)•in mathematics•2773 days 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 unique object in a possibly different set (ran...2
sinbad989(25)•in #mathematics•2777 days 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. We can actually extend the ideas of ordered ...2sinbad989(25)•in mathematics•2777 days 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. We can actually extend the ideas of ordered ...2
sinbad989(25)•in #mathematics•2778 days agoElements of Set Theory: RelationsElements of Set Theory: Relations First let's consider some examples. The ordering relation Thus we can say, that , relating 3 to 5. For this case, we have an a...2sinbad989(25)•in mathematics•2778 days agoElements of Set Theory: RelationsElements of Set Theory: Relations First let's consider some examples. The ordering relation Thus we can say, that , relating 3 to 5. For this case, we have an a...2
sinbad989(25)•in #mathematics•2779 days agoElements of Set Theory: Ordered PairsElements of Set Theory: Ordered Pairs Consider the following pair set: this can be thought as an unordered pair. Consider another pair set with additional infor...1sinbad989(25)•in mathematics•2779 days agoElements of Set Theory: Ordered PairsElements of Set Theory: Ordered Pairs Consider the following pair set: this can be thought as an unordered pair. Consider another pair set with additional infor...1
sinbad989(25)•in #mathematics•2781 days agoElements of Set Theory: Algebra of SetsElements of Set Theory: Algebra of Sets The two basic operation on sets are 1. operation of union 2. operation of intersection We also have the operation relati...1sinbad989(25)•in mathematics•2781 days agoElements of Set Theory: Algebra of SetsElements of Set Theory: Algebra of Sets The two basic operation on sets are 1. operation of union 2. operation of intersection We also have the operation relati...1
sinbad989(25)•in #programming•2802 days agoObject Oriented Programming: Specifying attributes and behaviorsSpecifying attributes and Behaviors We now have now added object-oriented terminology in our arsenal of definitions. We defined objects as instances of classes,...1sinbad989(25)•in programming•2802 days agoObject Oriented Programming: Specifying attributes and behaviorsSpecifying attributes and Behaviors We now have now added object-oriented terminology in our arsenal of definitions. We defined objects as instances of classes,...1
sinbad989(25)•in #mathematics•2805 days 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 two sets. And by repeating the process, we can...1sinbad989(25)•in mathematics•2805 days 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 two sets. And by repeating the process, we can...1
sinbad989(25)•in #mathematics•2807 days agoElements of Set Theory: AxiomsNow, we are done with the introduction chapter of the book, Elements of Set Theory. Again, I would like to emphasize the importance of the axiomatic method whic...0sinbad989(25)•in mathematics•2807 days agoElements of Set Theory: AxiomsNow, we are done with the introduction chapter of the book, Elements of Set Theory. Again, I would like to emphasize the importance of the axiomatic method whic...0
sinbad989(25)•in #mathematics•2807 days 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 the theory of abstract sets, as objects to b...1sinbad989(25)•in mathematics•2807 days 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 the theory of abstract sets, as objects to b...1
sinbad989(25)•in #mathematics•2808 days agoElements of Set Theory: NotationElements of Set Theory: Notation To denote sets, we will use a variety of letters, both lowercase (a,b,...), uppercase (A,B,...), and even script letters and Gr...1sinbad989(25)•in mathematics•2808 days agoElements of Set Theory: NotationElements of Set Theory: Notation To denote sets, we will use a variety of letters, both lowercase (a,b,...), uppercase (A,B,...), and even script letters and Gr...1
