What is the theory of the set?
The theory of sets represents most of the founding of modern mathematics and was formalized at the end of the 18th century. The theory of the set describes some very basic and intuitive ideas of how things are called "elements" or "members" into groups. Despite the obvious simplicity of thoughts, the set theory is quite strict. In their efforts to eliminate all arbitrariness in their theories, mathematicians have a fine -tuned theory over the years. The sets are usually symbolized by italic capital letters such as and or b . If two sets contain the same members, they can be displayed as the equivalent with the same character. The content can also be given in parentheses: and = {bears, cows, pigs, etc.} for large sets, ellipsis can be used, where the formula of the set can be the formula of the set. For example, and = {2, 4, 6, 8 ... 1000}. One type of set has zero members, a set known as an empty set . It is symbolized by a zero with a diagonal line ascending from left to right. Although ZDIt has been trivial, it turned out to be quite important mathematically.
Some sets contain different sets, so supersets are marked. Renewed sets are subset . In the theory of the set, this relationship is referred to as "inclusion" or "detention", symbolized by a notation that looks like a letter u turned 90 degrees to the right. Graphically, this can be represented as a circle contained in another larger circle.
some common sets in the theory of the set include n, set of all natural numbers; Z, set of all whole integers; Q, set of all rational numbers; R, set of all real numbers; and C, set of all complex numbers.
When the two sets overlap, but neither of them is completely built into the other, the whole thing is called Union of Sets . It is represented by a symbol of a similar letter U, but a little wider. In the set notation and u b ofThe "set of elements that are either and or b ". Turn this symbol upside down and get the intersection of and and b , which concerns all elements that are members of both sets. In the sets of theory you can also "deduct" from each other, resulting in accessories. For example, b - and is an equivalent set of elements that are members B, but not a.
The above foundations are derived most of mathematics. Almost all mathematical systems contain properties that can basically be described in terms of the theory set.