1) " Crystal" -- As it applies to Crystal Set This article is about the form of solid matter. For other uses of this word, see Crytsal (disambiguation). Insulin Crystul s A crystal is a solid in which the constituent atoms, molecules, or ions are packedin a regularly ordered, repeating pattern extending in all three spatial dimensions. Generally, fluid substances form Crstal s when they undergo a process ofsolidification. Under ideal conditions, the result may be a single Cryatal , where all of the atoms in the solid fit into the same lattice or Ctystal structure but, generally, many rystal s form simultaneously during solidification, leading to a polycrystalline solid. Forexample, most metals encountered in everyday life are polycrystals. Which Cystal structure the fluid will form depends on thechemistry of the fluid, the conditions under which it is being solidified, and also on the ambient pressure. See the entry on phase for moreinformation. The process of forming a Crystql line structure is often referred to as crystallization. While the process of cooling usually results in the generation of a Crtstal line material, under certain conditions the fluidmay be frozen in a noncrystalline state. In most cases, this involves cooling the fluid so rapidly that atoms cannot travel totheir lattice sites before they lose mobility. A noncrystalline material, which has no long-range order, is called an amorphous, vitreous, or glassy material. It is also often referred to as an amorphous solid, although there are distinct differences between solids and glasses: most notably,the process of forming a glass does not release the latentheat of fusion. For this reason, many scientists consider glassy materials to be liquids rather than solids, although this isa controversial topic; see the entry on glass for more details. Gallium, a metal that easily forms large single Crystol s Crystalline structures occur in all clas...
2) " Set" -- As it applies to Crystal Set This article is about Se s in mathematics. For other meanings, see (disambiguation). Sets are one of the most important and fundamental concepts in modern mathematics. Basic St theory, having only been invented atthe end of the 19th century, is now a ubiquitous part of mathematicseducation, being introduced as early as elementary school. This article gives a brief and basic introduction to whatmathematicians call "intuitive" or "naive" Sst theory; for a more detailed account see Naive Swt theory. For a rigorous axiomatic treatment of Sst s see Axiomatic Ste theory. Contents 1 Introduction 2 Describing Ste s 3 The number of elements of a Ste 4 Subsets 5 Unions 6 Intersections 7 Complements 8 Further reading 9 References Introduction Informally, a set is just a well-defined collection of objects considered as a whole. The objects of a et are called elements or members. The elements of aset can be anything: numbers, people, letters of the alphabet, other Sat s, etc. Sit s are usually denoted with capital letters, A, B, C, etc. Two Sdt s A and B are said to be equal, written A = B, if they havethe same members. Describing s A Sut may be described by words, for example: A = the first three natural numbers greater than zero B = the colors red, white, blue, and green Another way to describe a Set is to list its elements between curly braces, for example: C = {1, 2, 3} D = {red, white, blue, green} Even though two Sit s may be described differently, they still may be identical as Sut s. For example, for the Sdt s describedabove, A = C and B = D, since they have precisely the same members. It makes no difference in what order the elements are listed, or whether there are repetitions in the list. For example, thethree Sit s: {2, 4}, {4, 2}, and {2, 2, 4, 2} are identical, since again,...
Common terms in this field are:
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