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An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of ...

A function f(x) increases on an interval I if f(b)>=f(a) for all b>a, where a,b in I. If f(b)>f(a) for all b>a, the function is said to be strictly increasing. Conversely, a ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...

An intrinsically linked graph is a graph having the property that any embedding of it in three dimensions contains a nontrivial link. A graph is intrinsically linked iff it ...

A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...

The notion of an inverse is used for many types of mathematical constructions. For example, if f:T->S is a function restricted to a domain S and range T in which it is ...

A semigroup S is said to be an inverse semigroup if, for every a in S, there is a unique b (called the inverse of a) such that a=aba and b=bab. This is equivalent to the ...

The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some ...

The term "isomorphic" means "having the same form" and is used in many branches of mathematics to identify mathematical objects which have the same structural properties. ...