The American black bear (Ursus americanus) is a medium-sized bear native to North America. It is the continent's smallest and most common bear species. Black bears are omnivores, with their diets varying greatly depending on season and location. They typically live in largely forested areas, but do leave forests in search of food. Sometimes they become attracted to human communities because of the immediate availability of food. The American black bear is listed by the IUCN as Least Concern, due to the species' widespread distribution and a large global population estimated to be twice that of all other bear species combined. American black bears often mark trees using their teeth and claws as a form of communication with other bears, a behavior common to many species of bears.

The brown bear (Ursus arctos) is a large bear distributed across much of northern Eurasia and North America. It can weigh from 300 to 780 kilograms (660 to 1,700 lb) and its largest subspecies, the Kodiak Bear, rivals the polar bear as the largest member of the bear family and as the largest land-based predator.

There are several recognized subspecies within the brown bear species. In North America, two types are generally recognized, the coastal brown bear and the inland grizzly, and the two types could broadly define all brown bear subspecies. Grizzlies weigh as little as 350 lb (159 kg) in Yukon, while a brown bear, living on a steady, nutritious diet of spawning salmon, from coastal Alaska and Russia can weigh 1,500 lb (682 kg). The exact number of overall brown subspecies remains in debate.

While the brown bear's range has shrunk, and it has faced local extinctions, it remains listed as a least concern species by the IUCN, with a total population of approximately 200,000. Its principal range countries are Russia, the United States (mostly in Alaska), Canada, the Carpathian region (especially Romania, but also Ukraine, Slovakia, and so on), the Balkans, Sweden and Finland, where it is the national animal. The brown bear is the most widely distributed of all bears.

Defined broadly, a visionary, is one who can envision the future. For some groups this can involve the supernatural

The visionary state is achieved via meditation, drugs, lucid dreams, daydreams, or art. One example is Hildegard of Bingen, a 12th century artist/visionary and Catholic saint. Other visionaries in religion are Mohammed, St Bernadette and Joseph Smith (said to have had a vision of and communed with the Angel Gabriel), the Blessed Virgin), and the Angel Moroni respectively).

In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input.

Formal definitions, first devised in the early 19th century, are given below. Informally, a function f assigns an output f(x) to every input x. The function has a limit L at an input p if f(x) is "close" to L whenever x is "close" to p. In other words, f(x) becomes closer and closer to L as x moves closer and closer to p. More specifically, when f is applied to each input sufficiently close to p, the result is an output value that is arbitrarily close to L. If the inputs "close" to p are taken to values that are very different, the limit is said to not exist.

The notion of a limit has many applications in modern calculus. In particular, the many definitions of continuity employ the limit: roughly, a function is continuous if all of its limits agree with the values of the function. It also appears in the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph of a function.