Posts Tagged ‘Math’
Thursday, October 15th, 2009
Complements in Set Theory
Description
A detailed tutorial on complements in set theory. Step by step tutorial including several examples of complements in set theory for reference.
Overview
In set theory, a complement is the opposite of something. It works a little like negation, in that the complement of a set is everything but that set. The way to find this is to subtract the set from its universe, which is a larger set that the set you are taking a complement of belongs to. You can think of your set as a subset of the universe.
Tags: complement, discrete math, elements, Math, negation, opposite, set, set theory, subset, universe
Posted in Discrete Math | 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, October 15th, 2009
Difference in Set Theory
Description
A detailed tutorial of difference in set theory. Step by step tutorial including several examples of difference in set theory for reference.
Overview
Difference is what you get after subtracting two numbers – or two sets. As with other examples of subtraction, order is very important for difference in set theory. Unless two sets are identical, you will end up with a different answer depending on the order. Difference is very often used in conjunction with union and intersection of sets or power sets.
Tags: difference, discrete math, element, empty set, intersection, Math, number, order, power set, set, set theory, subset, subtract, subtraction, union
Posted in Discrete Math | No Comments »
Tuesday, October 13th, 2009
Overview of Superelevation
Description
A detailed tutorial on superelevation. Step by step tutorial including a visual example of superelevation of a road for reference.
Overview
The superelevation of a road or of a railway is the difference in elevation between the two edges. A non-zero superelevation – meaning that the edges of the road or railway are at different heights – allows for a bank turn, letting vehicles traverse the turns at higher speeds than would otherwise be possible. Superelevation is sometimes referred to as the cant of a road or railway. An important calculation in superelevation is the maximum speed of a vehicle on a curved road. It is determined by the formula 
.
Tags: algebra, banked turn, camber, cant, cross slope, curved, edges, elevation, height, Math, railway, road, speed, superelevation, track, train, vehicle, zero
Posted in Algebra | No Comments »
Tuesday, October 13th, 2009
Introduction to Present Value
Description
A detailed tutorial on solving for the present value. Step by step tutorial including several examples of solving for the present value for reference.
Overview
Present value is the value on a given date of a future payment or series of future payments. It is typically discounted to reflect the time value of money, and sometimes other factors. Because of this, the main calculation for present value is simply the calculation for the time value of money. The time value of money can be found by using the compund interest formula, which can be mathematically expressed as 
. This is equal to the present value.
Tags: algebra, calculation, compound, formula, interest, investment, Math, money, present, risk, time, value
Posted in Algebra | No Comments »
Tuesday, October 13th, 2009
How to Locate the Origin of a Graph
Description
A detailed tutorial on locating the origin of a graph. Step by step tutorial including several examples of how to locate the origin for reference.
Overview
The origin in mathematical terms means the center. Typically, the term origin is used with a graph in the Cartesian coordinate system. When on a graph, the origin is found at the point (0, 0), where the x-axis and y-axis intersect. Other common things to hear an origin being attributed to are geometrical shapes, most often a circle.
Tags: arithmetic, axis, cartesian, center, circle, coordinate, geometrical, graph, intersect, Math, middle, origin, shape, x, y
Posted in Arithmetic | No Comments »
Tuesday, October 13th, 2009
How to Identify Contradictions
Description
A detailed tutorial on identifying contradictions. Step by step tutorial including several examples of how to identify contradictions for reference.
Overview
A contradiction is a statement of only false values – one that is false no matter how you look at it. In terms of mathematical logic, it is defined as a propositional form that is false for every assignment of truth values to its components. In order for a statement to be a contradiction, when the proposition is on a truth table it must be false for every possible combination of P and Q.
Tags: components, contradiction, discrete math, false, logic, Math, P, proposition, Q, statement, tautology, true, truth table
Posted in Discrete Math | No Comments »
Tuesday, October 13th, 2009
How to Identify Tautologies
Description
A detailed tutorial on identifying tautologies. Step by step tutorial including several examples of how to identify tautologies for reference.
Overview
A tautology is a statement of truth – one that is true no matter how you look at it. In terms of mathematical logic, it is defined as a propositional form that is true for every assignment of truth values to its components. In order for a statement to be a tautology, when the proposition is on a truth table it must be true for every possible combination of P and Q.
Tags: components, contradiction, discrete math, false, logic, Math, P, proposition, Q, statement, tautology, true, truth table
Posted in Discrete Math | 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 13th, 2009
Power Sets in Set Theory
Description
A detailed tutorial on power sets. Step by step tutorial including several examples of power sets and how to perform operations of power sets for reference.
Overview
Power sets are defined as a set of all subsets. So for example, say you have a set A. The power set of A would be the set of all possible subsets of A. Power sets can also be used in normal operations, such as intersections and unions. All you do is find all possible subsets of both sets you are working with, and solve the problem like you would with a normal set.
Tags: difference, discrete math, element, empty set, intersection, Math, power, set, set theory, subset, union
Posted in Discrete Math | No Comments »
