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A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

The set difference A\B is defined by A\B={x:x in A and x not in B}. Here, the backslash symbol is defined as Unicode U+2216. The set difference is therefore equivalent to the ...

A pathwise-connected domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the ...

Given an ordinary differential equation y^'=f(x,y), the slope field for that differential equation is the vector field that takes a point (x,y) to a unit vector with slope ...

Let A be an n×n matrix over a field F. Using the three elementary row and column operations over elements in the field, the n×n matrix xI-A with entries from the principal ...

The term "snark" was first popularized by Gardner (1976) as a class of minimal cubic graphs with edge chromatic number 4 and certain connectivity requirements. (By Vizing's ...

As shown by Schnirelman (1944), a square can be inscribed in any closed convex curve, although it is not known if this holds true for every Jordan curve (Steinhaus 1999, p. ...

A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

For what value of x is f(x)=x^(1/x) a maximum? The maximum occurs at x=e, where f^'(x)=x^(-2+1/x)(1-lnx)=0, (1) which is zero at x=e and gives a maximum of ...

Let a_1=1 and define a_(n+1) to be the least integer greater than a_n which cannot be written as the sum of at most h>=2 addends among the terms a_1, a_2, ..., a_n. This ...