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CLASSIFICATION AND WAYS OF NAMING A SET

GRADE 7 MATHEMATICS QUARTER I

Objectives:

illustrate finite and infinite set;
differentiate equal and equivalent sets;
enumerate ways of naming a set.

UNLOCKING WORDS DIFFICULTY

INTEGERS

{-∞ , 0, +∞ }

WHOLE NUMBERS

{0, 1, 2, 3, 4, 5, 6, ... }

COUNTING/NATURAL NUMBERS

{1, 2, 3, 4, 5, 6,...}

EVEN NUMBERS

{2, 4, 6, ,8, 10,...}

ODD NUMBERS

{1, 3, 5, 7, 9,...}

PRIME NUMBERS

{2, 3, 5, 7, 11,...}

COMPOSITE NUMBERS

{4, 6, 8, 9, 10,...}

PERFECT SQUARES

{1, 4, 9, 16, 25,...}

MULTIPLES

{skip counting by...}

FACTORS

{Numbers which can be divided without remainder}

FINITE AND INFINITE SETS

A set is finite if the number of elements in a given set is a whole number {1, 2, 3,...N}, otherwise it is said to be infinite.
This means it has an end or last term. Consider the examples below.

a. ) Days of the week: {𝑆𝑢𝑛𝑑𝑎𝑦, 𝑀𝑜𝑛𝑑𝑎𝑦, 𝑇𝑢𝑒𝑠𝑑𝑎𝑦, . . . , 𝑆𝑎𝑡𝑢𝑟𝑑𝑎𝑦}

b. ) First 10 positive perfect squares: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }

On the other hand, an infinite sequence contains a countless number of terms.
The number of terms of the sequence continues without stopping or it has no end term.
The ellipsis (…) at the end of the following examples shows that the sequences are infinite. Consider the examples below.

a. ) Counting numbers: {1, 2, 3, 4, 5, . . .}

b. ) Multiples of 5: {5, 10, 15, 20, 15, . . .}

Finite Set - can be counted
Infinite Set - cannot be counted

EXAMPLE:

EXAMPLE 1: Counting numbers

A = {counting numbers}

A = { 1, 2, 3, 4, 5,...}

Set A is an INFINITE SET since there is a elipsis (...) in the end the given set

EXAMPLE 2: Counting numbers less than 5

B = {counting number less than 5}

B = { 1, 2, 3, 4}

Set B is a FINITE SET

EXAMPLE 3: Letters in the English Alphabet

C = {letters in the english alphabet}

C = {a, b, c, d, e, ..., x, y, z}

Set C is an FINITE SET

EXAMPLE 4: Whole numbers greater than 9

D = {whole number greater tha 9}

D = { 10, 11, 12, 13,...}

Set D is an INFINITE SET

EQUAL AND EQUIVALENT SETS

Two sets are EQUAL if and only if they contain exactly the same elements.
Two sets are EQUIVALENT if and only if there is a one-to-one correspondence between the sets

EXAMPLE OF EQUAL AND EQUIVALENT SETS:

A = {orange, apple, guava}

B = {guava, mango, apple}

C = {apple, guava, orange)

Set A and C are equal sets
Set A and B are equivalent sets.
Set B and C are equivalent sets.

ACTIVITY: EQUAL SETS OR EQUIVALENT SETS

ACTIVITY: Is it EQUAL SETS OR EQUIVALENT SETS?

A = {1, 2, 3, 4, 5}

B = {2, 3, 4, 6}

C = {3, 2, 4, 1, 5}

D = {1, 3, 5, 7, 9}

Set C and D are...?
Set A and C are...?
Set B and C are...?
Set A and D are...?

You may answer this via Gforms link:https://forms.gle/cgV1NyhhRJHSMJMp7

EXAMPLE OF ROSTER METHOD AND SET-BUILDER NOTATION:

Roster Method

A = {a, e, i ,o u}

B = {yellow, red, blue}

Set-builder Notation

C = {x/x is a letter in the Alphabet}

Read as "C is the set of all x such that x is a letter in the alphabet

WAYS OF DEFINING A SET

Roster Method

-listing the elements

-if the set does not contain a very large number of elements

Set-builder Notation

-describing the elements if there are many elements

VIDEO LESSON FOR BETTER UNDERSTANDING:

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