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Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

Discrete Mathematics

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

For a right triangle with legs a and b and hypotenuse c, a^2+b^2=c^2. (1) Many different proofs exist for this most fundamental of all geometric theorems. The theorem can ...

The anticomplementary triangle is the triangle DeltaA_1^'A_2^'A_3^' which has a given triangle DeltaA_1A_2A_3 as its medial triangle. It is therefore the anticevian triangle ...

Relaxation methods are methods of solving partial differential equations that involve splitting the sparse matrix that arises from finite differencing then iterating until a ...