Posts Tagged ‘open’
Thursday, December 31st, 2009
How to Write Step Functions
Description
A detailed tutorial on how to write step functions. Step by step tutorial including several examples of how to write step functions for reference.
Overview
A step function, also called a staircase function, is a finite linear combination composed of several different intervals. They are considered to be a piecewise constant function. The graph of a step function is often expressed as steps, or a staircase, which is how it got its name. It simply looks like several disconnected lines, with alternate open and closed ends so that it easily passes the vertical line test for functions.
Tags: closed, combination, constant, diconnected, discrete math, ends, finite, function, graph, intervals, line, linear, lines, open, piecewise, staircase, step, test, vertical
Posted in Discrete Math | No Comments »
Tuesday, December 29th, 2009
How to Identify a Disconnected Graph
Description
A detailed tutorial on how to identify disconnected graphs. Step by step tutorial including several examples of disconnected graphs for reference.
Overview
A disconnected graph is a graph where not every single vertex is connected to all other vertices. Typically, graphs will have paths from all vertices, but if there is not a direct path from each and every vertex, then it is considered to be a disconnected graph. Some common shapes that are seen that are disconnected graphs are stars, rectangles, and hexagons. The opposite of a disconnected graph is a connected graph.
Tags: closed, connected, direct, disconnected, discrete math, edge, graph, hexagon, open, opposite, path, rectangle, shape, star, triangle, vertex, vertices, walk
Posted in Discrete Math | No Comments »
Tuesday, December 29th, 2009
How to Identify a Connected Graph
Description
A detailed tutorial on how to identify connected graphs. Step by step tutorial including several examples of connected graphs for reference.
Overview
A connected graph is a graph where every single vertex is connected to every other vertex. This does not mean to simply have a clear path from one vertex to another – it means there needs to be a direct path, or an edge, between two vertices. A triangle is a commonly seen shape that is a connected graph. The opposite of a connected graph is a disconnected graph.
Tags: closed, connected, direct, disconnected, discrete math, edge, graph, hexagon, open, opposite, path, rectangle, shape, star, triangle, vertex, vertices, walk
Posted in Discrete Math | No Comments »
Tuesday, November 17th, 2009
Introduction to Half-Planes
Description
A detailed tutorial on half-planes. Step by step tutorial including several examples of half-planes for reference.
Overview
A half-plane is simply half a plane, that includes all the lines on half of the plane and sometimes the points. If the plane includes the points, it is a closed half-plane. If it doesn’t, then it is an open half-plane. The most common half planes are upper, lower, right, and left planes, where that side of the plane is all that is included. However, there are many other kinds of half planes that are all a variety of diagonal half-planes.
Tags: bottom, closed, Geometry, half, half-plane, left, lines, lower, open, plane, points, region, right, top, upper
Posted in Geometry | No Comments »
Tuesday, November 17th, 2009
How to Draw a Boundary Line
Description
A detailed tutorial on how to draw a boundary line. Step by step tutorial including several examples on how to draw a boundary line for reference.
Overview
A boundary line is used when graphing inequalities on a number line or a regular Cartesian graphing system. What the boundary line does is connect the two points in the inequality – in other words, it sets a boundary of what an unknown variable would be on that inequality. The boundary line can either be solid or dashed. The boundary line is only dashed when it is drawn on a regular graph, to express that the line was somewhere else at one point and was then moved. In all other cases, the boundary line is solid.
Tags: algebra, boundary, closed, coordinates, dashed, equal, graph, greater, inequality, interval, less, line, number, open, points, solid, then, to
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Introduction to Nested Intervals
Description
A detailed tutorial on nested intervals and the nested interval theorem. Step by step tutorial including several examples of nested intervals for reference.
Overview
Nested intervals means to have one interval (or multiple intervals) inside of another interval. The intervals will get smaller and smaller the more you add, until they will finally dimish entirely. There is a theorem for nested intervals, called the nested interval theorem. It states that if A_n = [a_n, b_n] is a sequence of closed intervals such that A_n+1 is a subset of A_n for all n belonging to the set of natural numbers, then the union over A_n is not an empty set.
Tags: algebra, closed, empty, interval, natural, nested, number, open, sequence, set, subset, theorem
Posted in Algebra | No Comments »
Thursday, October 15th, 2009
Definition of Open and Closed Intervals
Description
A detailed tutorial on open and closed intervals. Step by step tutorial including several examples of open and closed intervals for reference.
Overview
An interval is a set of real numbers, expressed by an ordered pair. There are two types of intervals, open intervals and closed intervals. An open interval is an interval written with parenthesis. It implies that the endpoint is not included in the set. A closed interval is an interval written with brackets. It implies that the endpoint is included in the set. It is possible for one endpoint of an interval to be closed, and for the other to be open.
Tags: algebra, bounded, brackets, closed, coordinates, element, endpoint, interval, Math, open, ordered pair, parenthesis, real numbers, set
Posted in Algebra | No Comments »
Thursday, September 24th, 2009
An Overview of Rolle’s Theorem
Description
A detailed tutorial on how to solve problems using Rolle’s Theorem. Step by step tutorial including examples of how to solve problems using Rolle’s Theorem for reference.
Overview
Rolle’s Theorem is a special instance of the Mean Value Theorem, and can be used to prove the Mean Value Theorem. Rolle’s Theorem states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero. Mathematically this can be expressed as if a real-valued function f is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists a c in the open interval (a, b) such that f ‘(c) = 0.
Tags: Calculus, closed, continuous, differentiable, function, graph, interval, Math, mean value theorem, open, real-valued function, rolle's theorem, slope, tangent line, zero
Posted in Calculus | No Comments »
