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Contribution of mathematician

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- 1. CENTRAL UNIVERSITY OF HARYANA DEPARTMENT OF TEACHER EDUCATION Course- pedagogy of mathematics Course code- SOE 02 02 07 DCEC 3104 ASSIGNMENT ON —SETS SUBMITTED BY BICHITRA KUMARI DASH. 221831 SEC - A SUBMITTED TO Dr. Mahendar kakkerla
- 2. INTRODUCTION In Maths, sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}. For example, set A is a collection of all the natural numbers, such as A = {1,2,3,4,5,6,7,8,…..∞}. Also, check sets here. Sets can be represented in three forms: Roster Form: Example- Set of even numbers less than 8={2,4,6} Statement Form: Example-A = {Set of Odd numbers less than 9} Set Builder Form: Example: A = {x: x=2n, n ∈ N and 1 ≤ n ≤ 4}
- 3. CONTRIBUTION OF MATHEMATICIANS Georg Cantor was a popular German mathematician. He is best known as the inventor of set theory that later became a fundamental theory in mathematics. He was able to establish the importance of one-to-one correspondence between members of two sets, well- ordered sets, and defined infinite sets. These proved that real numbers are much more numerous than natural numbers. Actually, his theorem implies the existence of ‘infinity of infinities.’ Georg also defined the ordinal and cardinal numbers and their arithmetic.
- 5. NATURE OF SETS A set is the mathematical model for a collection of different[1] things;[2][3][4] a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.[5] The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same element
- 6. GAMES AND ACTIVITIES ● Catch Me ● Materials ● Index cards with one set notation symbol on each ● You will need one card per student so replicas will be necessary, however, try to keep the numbers of each symbol equal. ● Preparation ● Write the six sets above on the board. ● Instructions ● Hand out one card to each student. ● Stand at the board and ask students to stand in a line against the opposite wall of the room. ● Call out instructions for students to move toward you based on their card identification. For example: ● ''Move one step forward if your card means to create a new set out of all the numbers in two other sets.'' ● ''Hop forward twice if your card would result in the set {4}.'' ● For clues that could have more than one response (like subset or intersection), ask students to explain why they have moved forward. ● The first student to reach you takes your place while the other students return to the starting place. ● Play as long as time allows swapping leaders each time a student reaches the leader.
- 7. TLM RELATED SETS ● Chart paper ● Working model ● Using flash cards ● Using different concrete objects ● Using colour chalks
- 8. OPEN ENDED QUESTIONS ON SETS ● How the concept of sets helps you in your real life? ● What is the major differences among types of sets ? ● How do you describe operations on sets ?
- 9. CONCLUSION Sets and subsets are some basics of pure mathematics and this leads to higher modern algebra. You can take real-life examples for this topic instead of numerical or variables. You can show how the symbols of belongs to, contained and other popular symbols used in mathematics. Let’s take an example of the classroom, where a teacher and the students belong to the set called classroom and the classroom is a subset of the school. You can conclude the sets are applicable to the whole universe. Sets are generally useful for logical and aptitude problems.