 Get a clear concept of Sets from our maths tuition # 22 Jun Get a clear concept of Sets from our maths tuition

Sets may just be the oldest and most common topic or concept in the history of maths tuition. A set is a collection of items. A more generic definition of a set would define it as a group of well-defined and unique items that are related, considered as an object in its capacity. The concepts of sets is a core principle in maths syllabi and students need to understand and appreciate them in their basic form before any complex associated concepts can be learnt.

### Classes of Sets

There are many classes of sets but the classification is dependent on what nature of sets you wish to address. In math tuition, you could classify sets according to the quantity they hold. In this context, there are three 3 types of sets namely; finite sets, infinite sets, and null sets.

•           A finite set is one whose elements are countable or quantifiable. These have a limited number of elements. A natural number can be used when giving the quantity of a finite set. It would be incorrect to give a negative figure when referring to the elements a set holds. An example of a finite set would be the number of fingers on a person’s hand. The number will always be limited not a negative. The number of physical items can never be negative.
•           For the infinite set, as the name suggests, the elements are infinity in counting. It is impossible to give a correct figure when referring to such sets. The set typically grows continuously at an uncontrolled rate, for example, the grains of sand on the planet. Rocks are constantly eroded to produce this sand so it is impossible to give a standard figure even if we could count them. It may also be because the set’s contents are impossible to count.
•     The third one is the null set. This set is commonly known as an empty set. There is no element existent in it. When a set’s quantity reaches zero it becomes an empty set. A real-life example would be the number of animals that live in outer space. It is scientifically proven that life cannot exist beyond the earth’s atmosphere.

Sets can also be classified according to their relationship. In this class, we have several subclasses which are; equivalent sets, subsets, disjoint sets, subset, proper subset, power set, and universal set.

•           Equivalent sets are sets with the same number of items. These sets, 2 or more, share the same number of items but different elements. An example would be the set of fingers in the right hand and a set of fingers in the left hand. Both are five.
•           Subsets are sets within a set. An example would be transport modes as the major set. Subsets would be air, water, and land. They are smaller classifications of a larger set. Sometimes a subset may contain all the elements of a set. An example would be a boys-only high school with the set class. This type of subset is called an improper subset. Using gender we may have a subset for boys and a subset for girls.  All elements would be in the subset of boys. A set may have a subset and that subset may also carry other subsets. An example would be animals. There are water, air, and land animals. In the land animals’ set, there are subsets with herbivores, carnivores, and omnivores. In the carnivores’ set, we have the cat family, dog family, reptiles and so on.
•      A subset with some elements within the parent set is called a proper set. A proper set is a subset containing some but not all elements in the same as its parents set. An example would be set A = {a, b, c, d, e, f}, and the B = {c, f}. There is also a situation where subsets intersect or share the same elements. An example would be crocodiles. They are both water and land animals.
• Disjoint sets are sets (often subsets) that have no elements in common at all. An example would be natural organisms. There are animals and plants but there is no element in common. They do not share any attributes except for the parent set. This parent set is also known as the universal set. It is the ultimate set from which all subsets originate. Note that it is possible to have elements in the universal set that are not part of any subsets.

All these sets apply in real life situations as exemplified above. They also apply in abstract studies and theories and are popular for often bringing order to seemingly chaotic data. As such, sets are one of the most fundamental topics in maths tuition that you will constantly run into across all scientific and most non-scientific fields of study.

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