Posts Tagged ‘unique’
Thursday, November 19th, 2009
Overview of the Cost Function
Description
A detailed tutorial on the cost function. Step by step tutorial including several examples of the cost function for reference.
Overview
The cost function is a name for a function that is being used in optimization. It is a very important part of an optimization problem. The cost function can be any graph, because all it refers to is the function – the function could be different every time, and it could still be called the cost function. What we learn from this is that the cost function is not unique.
Tags: algebra, constraints, cost, domain, energy, function, functional, graph, linear, maximize, minimize, objective, optimization, solution, unique, variable
Posted in Algebra | No Comments »
Tuesday, November 17th, 2009
Overview of Sides and Bases of Polyhedrons
Description
A detailed tutorial on sides and bases of polyhedrons. Step by step tutorial including several examples of sides and bases of polyhedrons for reference.
Overview
Sides and bases of polyhedrons are more commonly known as faces of 3D geometrical shapes. Typically on a polyhedron you will have 2 bases and several sides, although there are exceptions to that rule. The cylinder only has one side, and the triangular prism, or pyramid, only has one base. You can identify the base because it is a unique shape on the polyhedron. Everything else is a side. This only applied to your normal polyhedron shapes such as prisms.
Tags: 3D, bases, cylinder, faces, figure, geometrical, Geometry, polyhedron, prism, rectangular, regular, shape, sides, triangular, unique
Posted in Geometry | No Comments »
Friday, November 6th, 2009
Introduction to Injective and Surjective Functions
Description
A detailed tutorial on injective and surjective functions. Step by step tutorial including several examples of injective and surjective functions for reference.
Overview
When given a function, there are two properties it can possess: it can be either injective or surjective. An injective function is a function that associates distinct arguments in one domain with distinct values in one codomain, and every unique argument produces a unique result. A surjective function is a function where the range is equal to the codomain. A surjective function is also called a surjection or said to be onto. For both cases, the function could be bijective if all elements in the codomain are mapped, which means that it would be both injective and surjective at the same time.
Tags: algebra, arguments, bijective, codomain, equal, function, injective, mapped, onto, range, subjection, surjective, unique, values
Posted in Algebra | No Comments »
Thursday, October 29th, 2009
Successor Properties of Natural Numbers
Description
A detailed tutorial on the successor properties of natural numbers. Step by step tutorial including several examples of the successor properties of natural numbers for reference.
Overview
The successor properties are one of eight sets of properties of natural numbers. The successor properties deal with the actual set of natural numbers, not just parts of the set. It especially concerns the placement of the number 1 in the set of natural numbers. As the term successor implied, these properties deal with what numbers are successors of other numbers. They can be proven by the definition of a successor and the set of natural numbers.
Tags: -1, after, arithmetic, follows, natural, number, properties, set, successor, unique, x
Posted in Arithmetic | No Comments »
Tuesday, October 13th, 2009
Empty Set in Set Theory
Description
A detailed tutorial on the empty set. Step by step tutorial including several examples and a description of the properties of the empty set for reference.
Overview
The empty set is a unique set in set theory that means a set composed of nothing. In an empty set, there are no elements at all. The empty set has one very unique property – it is the subset of all sets. The set of all natural numbers up to infinity? It’s a subset. The set of prime numbers less than 20? It’s a subset of that, too. It is also a subset of itself – although that is not particurarly unique. The empty set is not used in equations, but can be used to define them.
Tags: difference, discrete math, element, empty set, intersection, Math, none, set, set theory, subset, union, unique, zero
Posted in Discrete Math | No Comments »
Tuesday, October 6th, 2009
Introduction to Tree Diagrams
Description
A detailed tutorial on how to make tree diagrams. Step by step tutorial including several examples of how to make tree diagrams for reference.
Overview
A tree diagram is a specific type of diagram that is often used to organize items and possibilities. It has a unique network topology. It can be seen as a type of network diagram, which can in turn be seen as a cluster diagram. Tree diagrams are very useful when trying to figure out probabilities and statistics.
Tags: algebra, cluster, diagram, Math, network, organize, possibilities, probabilities, statistics, topology, tree, unique
Posted in Algebra | No Comments »
Tuesday, October 6th, 2009
Definition of a Uniqueness Theorem
Description
A detailed tutorial on the uniqeness theorem. Step by step tutorial including several examples of how to solve a uniqueness theorem for reference.
Overview
A uniqueness theorem is any mathematical theorem that states only one mathematical object satisifies special conditions – that is, that a problem only has one solution, a unique solution. Sometimes the solution to the equation is also determined uniquely – that is, there is only way to solve the problem, instead of multiple ways.
Tags: arithmetic, condition, existence, Math, solution, solve, theorem, unique, uniqueness
Posted in Arithmetic | No Comments »
Tuesday, September 29th, 2009
How to Use Cramer’s Rule
Description
A detailed tutorial on how to solve systems of equations using Cramer’s rule. Step by step tutorial including several examples of how to solve for systems of equations using Cramer’s rule for reference.
Overview
Cramer’s rule is a theorem in linear algebra that is used as an alternative method of solving systems of equations. Cramer’s rule uses matrices to solve for systems of equations, and is typically used when there is a unique solution. The solution is expressed in the form of matrices which are obtained by replacing one column of the vector of right hand sides of the equations.
Tags: algebra, Cramer's rule, Gabriel Cramer, linear algebra, linear equations, Math, matrices, matrix, systems of equations, unique, vector
Posted in Algebra | No Comments »
Tuesday, September 15th, 2009
An In-Depth Look at the Closure Property
Description
A detailed tutorial on how to use the closure property. Step by step tutorial including several examples of how to use the closure property for reference.
Overview
The closure property states that if a and b are both real numbers, then a + b is a unique real number, and a * b is also a unique real number. Basically what the closure property is saying is that if you add or multiply two real numbers, your only possible answer is a real number. The closure property is also saying that the sum or product of two real numbers is unique, meaning there is only one number that it could be.
Tags: add, addition, arithmetic, closure, closure property, Math, multiplication, multiply, product, property, real numbers, sum, unique
Posted in Arithmetic | No Comments »
