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In particular, one can no longer talk about the limit of a function at a point, but rather a limit or the set of limits at a point. A function is continuous at a limit point p of and in its domain if and only if f(p) is the (or, in the general case, a) limit of f(x) as x tends to p. There is another type of limit of a function, namely the ...
In extremal graph theory, the forbidden subgraph problem is the following problem: given a graph , find the maximal number of edges (,) an -vertex graph can have such that it does not have a subgraph isomorphic to .
An important class of functions when considering limits are continuous functions. These are precisely those functions which preserve limits , in the sense that if f {\displaystyle f} is a continuous function, then whenever a n → a {\displaystyle a_{n}\rightarrow a} in the domain of f {\displaystyle f} , then the limit f ( a n ) {\displaystyle ...
The first problem is the so-called graph realization problem, and the second is known as the digraph realization problem. The bipartite realization problem is equivalent to the question, if there exists a labeled bipartite subgraph of a complete bipartite graph to a given degree sequence.
In a graph, a maximum cut is a cut whose size is at least the size of any other cut. That is, it is a partition of the graph's vertices into two complementary sets S and T, such that the number of edges between S and T is as large as possible. Finding such a cut is known as the max-cut problem. The problem can be stated simply as follows.
A limit of a sequence of points () in a topological space is a special case of a limit of a function: the domain is in the space {+}, with the induced topology of the affinely extended real number system, the range is , and the function argument tends to +, which in this space is a limit point of .
The Hayflick limit, or Hayflick phenomenon, is the number of times a normal somatic, differentiated human cell population will divide before cell division stops. [ 1 ] [ 2 ] The concept of the Hayflick limit was advanced by American anatomist Leonard Hayflick in 1961, [ 3 ] at the Wistar Institute in Philadelphia , Pennsylvania.
create limits for F if whenever (L, φ) is a limit of GF there exists a unique cone (L′, φ′) to F such that G(L′, φ′) = (L, φ), and furthermore, this cone is a limit of F. reflect limits for F if each cone to F whose image under G is a limit of GF is already a limit of F. Dually, one can define creation and reflection of colimits.