Posts Tagged ‘x’
Thursday, December 24th, 2009
Finding the Function of a Directed Graph
Description
A detailed tutorial on finding the function of a directed graph. Step by step tutorial including several examples of finding functions of digraphs for reference.
Overview
A directed graph, more commonly known as a digraph, is the visual representation of a function or of a relation. As in any graph, there are points and lines – called vertices and edges in a digraph. Each edge has an arrow pointing to a vertex. The first vertex – the one the arrow comes from – is the x coordinate of an ordered pair. The second vertex – the one the arrow is pointing to – is the y coordinate of an ordered pair. In the case of double-sided arrows, two ordered pairs are made, with the x and y coordinates switching. This is done for every single vertex and edge on the graph.
Tags: arrow, coordinate. ordered, digraph, directed, discrete math, double, edges, expression, First, function, graph, lines, pair, points, relation, representation, second, side, vertex, vertices, visual, x, y
Posted in Discrete Math | No Comments »
Thursday, December 10th, 2009
Inverse Image of Sets
Description
A detailed tutorial on the inverse image of sets. Step by step tutorial on the inverse image of sets for reference. Knowledge of the inverse image of sets is important in advanced discrete mathematics courses.
Overview
Say that you have a function f: A –> B. Then, X is a subset of A and Y is a subset of B. The image of X or the image set of X is f(X) = {y belongs to B: y = f(x) for some x belonging to X}. The inverse image of Y is defined as f^-1(Y) = {x belongs to A: f(x) belongs to Y}. The inverse image is simply a reversed form of the image. Often when asked to find the inverse image, it will help to set up a drawing of the image of the function, connecting everything where it needs to go. Then to find the inverse you simply reverse your work.
Tags: a, b, connect, diagram, discrete math, form, function, image, image set, inverse, mapping, picture, reverse, set, subset, x, y
Posted in Discrete Math | No Comments »
Friday, November 20th, 2009
Overview of the Preimage of a Set
Description
A detailed tutorial on the preimage of a set. Step by step tutorial including several examples of the preimage of a set for reference.
Overview
The preimage of a set is defined over a function. If there is a function over A and B, then we can say that y = f(x), provided that (x, y) belongs to f. Based on this definition, x is the preimage of y under f. To find the preimage, simply look for the value of x that matches with the proper value of y in any function of ordered pairs in A and B.
Tags: a, b, belongs, coordinates, defined, definition, discrete math, f, function, image, ordered pairs, preimage, set, theory, value, x, y
Posted in Discrete Math | No Comments »
Friday, November 20th, 2009
How to Pick Variables
Description
A detailed tutorial on how to pick variables. Step by step tutorial including several examples of how to pick variables for reference.
Overview
Variables are letters picked to represent unknown values in expressions and equations. Usually they are lowercase, but they can be made uppercase. When trying to pick a variable, you must choose wisely. x is the most common variable, followed by n. x is picked because people associate it with the unknown, and n is picked because it stands for “number.” The variable should be easily recognizable – you should not use a variable that looks like another number or some symbol of a mathematical operation. You should check to see what is included in your equation – for instance, m stands for slope, so if you are doing an equation with slope you need to pick a different variable to avoid confusion. And you should always pick a variable that makes sense – the first letter of your subject matter usually works quite well.
Tags: a, algebra, b, c, choose, equation, expression, lowercase, m, mathematical, n!, number, operation, slope, symbol, unknown, uppercase, value, variable, variables, x, y, z
Posted in Algebra | No Comments »
Thursday, November 19th, 2009
The X and Y Axis on a Cartesian Graph
Description
A detailed tutorial of the x axis and the y axis. Step by step tutorial including several examples of the x axis and the y axis for reference.
Overview
The the Cartesian coordinate system, there is an x axis and a y axis. The x axis runs horizontally across the system and all first terms in ordered pairs are x coordinates, from the x axis. The y axis runs vertically across the system and all second terms in ordered pairs are y coordinates, from the y axis. The x and y axis work together to use a pattern of right angles and perpendicular lines in order to find ordered pairs and coordinates of x and y on the graph.
Tags: algebra, angle, axis, basic, cartesian, coordinate, graphing, graphs, horizontal, lines, ordered, pairs, perpendicular, right, system, vertical, x, y
Posted in Algebra | No Comments »
Friday, October 30th, 2009
How to Determine the Point of Discontinuity
Description
A detailed tutorial on determining the point of discontinuity. Step by step tutorial including several examples of how to determine the point of discontinuity for reference.
Overview
A point of discontinuity is where the graph of a function is discontinuous – this means the graph has a breaking point in it, it break off for a while and starts again somewhere else, or there is a small open circle somewhere on the graph, which would be an actual point of discontinuity. In mathematical terms, the point of discontinuity is the point at which the graph of the function is undefined. Simply look a value of x that will make the function undefined, and that is your point of discontinuity. This is easiest to determine when your function is a fraction.
Tags: a, algebra, break, discontinuity, discontinuous, fraction, function, graph, point, start, stop, undefined, x
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 »
Thursday, October 29th, 2009
Order Properties of Natural Numbers
Description
A detailed tutorial on the order properties of natural numbers. Step by step tutorial including several examples of the order properties of natural numbers for reference.
Overview
The order properties are one of the eight sets of properties of natural numbers. The order properties are all based off of inequalities and how to order inequalities. Less than and less than or equal to are the two that are used in the order properties. There are five order properties in all. Since the order properties are of natural numbers, in order to prove the order properties your examples must be natural numbers, or positive integers greater than or equal to one.
Tags: arithmetic, equal, greater than, greater than or equal to, inequalities, less than, less than or equal to, n!, natural, number, order, property, x, y, z
Posted in Arithmetic | No Comments »
Thursday, October 29th, 2009
Overview of Quasitransitive Relations
Description
A detailed tutorial on the property of quasitransitive relations. Step by step tutorial including several examples of quasitransitive relations for reference.
Overview
A quasitransitive relation can be mathematically defined as for all x, y, and z belonging to A, if x R y, y R z, ~(y R x), and ~(z R y), then x R z and ~(z R x). In this statement, A is a set, and R is a relation of that set. A quasitransitive relation is considered to be a weak version of a transitive relation. If the relation also happens to be asymmetric, then it is considered transitive.
Tags: arithmetic, asymmetric, negation, opposite, property, quasitransitive, r, relation, transitive, x, y, z
Posted in Arithmetic | No Comments »
Thursday, October 29th, 2009
Overview of Symmetric Relations
Description
A detailed tutorial on the property of symmetric relations. Step by step tutorial including several examples of symmetric relations for reference.
Overview
A symmetric relation can be mathematically defined as for all x, y, and z belonging to A, if x R y and y R z, then x R z. In this statement, A is a set, and R is a relation of that set. An empty set is considered to be symmetric. Since a symmetric relation is defined by a conditional sentence, a proof for the symmetric property of relations would be written as a direct proof.
Tags: conditional, direct, discrete math, empty, equal, equivalence, married, odd, proof, property, r, relation, set, symmetric, x, y
Posted in Discrete Math | No Comments »
