My Math Blog

  Thus a rational number with an irrational as an exponent is rational.

The types of numbers: Representation of Ranges: a<x<=b == (a,b]

 A list of useful derivatives of trigonometric identities:

Differentiation is a method to find the "Rate of Change" or "Change Per Unit Time" of an equation, this can mean the change in distance on a journey per hour, the change in volume of water in a leaking tub per minute, or even the change in distance of an accelerating race car per second. These results can be expanded further: finding the velocity of an accelerating ball at a certain distance, finding the current change in volume of a tub of water at a specific height, the finding the maximum area of an object with a constant perimeter, and more. As long as there is a change in a measurement that correlates to the change of another measurement, differentiation can be of use. First and foremost, the differentiated result of a function is known as a derivative. For example, speed can be considered the "Change of Distance Per Unit Time", so speed is the 'Derivative of Distance". Second of all, the amount of times something can be differentiated is inf...

Where Vector means " determining the position of one point in space relative to another". Things to note: 1) While not always the case, Point O is usually considered the origin point, meaning that it's position in 2 dimensional space is (0,0). 2) Due to the limitations of digital text, any Vector going by the naming convention of XY where X and Y are points, implies a Vector Line from Point X to Point Y. Where it would usually look, for OA, like: 3) Vector Lines can be added together, the rule being that the end point of one must be the beginning point of the next, for example: OA + AB = OB, since OA is the vector from Point O to Point A, then AB is the vector from Point A to Point B, adding them together creates a vector that goes from Point O to Point A to Point B. 4) Vectors can also be denoted in a Variable-like fashion, for example OA can be denoted as "a". Thus these Vectors can be arranged in an equation to form the Vector of one point to another. For exa...