`\color{purple}ul(✓✓) \color{purple} " DEFINITION ALERT"`
A set which is empty or consists of a definite number of elements is called `"finite"` otherwise, the set is called `"infinite."`
`\color{green} "Consider some examples :"`
`(i)` Let `W` be the set of the days of the week. Then `W` is finite.
`(ii)` Let `S` be the set of solutions of the equation `x^2 –16 = 0`. Then `S` is finite.
`(iii)` Let `G` be the set of points on a line. Then `G` is infinite.
`\color{green} ✍️ \color{green} \mathbf(KEY \ POINTS)`
• When we represent a set in the roster form, we write all the elements of the set within braces `{ }.`
• It is not possible to write all the elements of an infinite set within braces `{ }` because the numbers of elements of such a set is not finite.
• So, we represent some infinite set in the roster form by writing a few elements which clearly indicate the structure of the set followed ( or preceded ) by three dots.
`"For example,"` `{1, 2, 3 . . .}` is the set of natural numbers,
` \ \ \ \ \ \ \ \ \ \ \ {1, 3, 5, 7, . . .} ` is the set of odd natural numbers,
` \ \ \ \ \ \ \ \ \ \ \ {. . .,–3, –2, –1, 0,1, 2 ,3, . . .}` is the set of integers. All these sets are infinite.
`\color{green} ✍️ \color{green} \mathbf(KEY \ POINTS)`
• All infinite sets cannot be described in the roster form.
• For example, the set of real numbers cannot be described in this form, because the elements of this set do not follow any particular pattern.
`\color{green} ✍️ \color{green} \mathbf( "Cardinality of a finite set" )`
`"Cardinality"` of a finite Set is defined as total number of elements in a set.
`\color{purple}ul(✓✓) \color{purple} " DEFINITION ALERT"`
A set which is empty or consists of a definite number of elements is called `"finite"` otherwise, the set is called `"infinite."`
`\color{green} "Consider some examples :"`
`(i)` Let `W` be the set of the days of the week. Then `W` is finite.
`(ii)` Let `S` be the set of solutions of the equation `x^2 –16 = 0`. Then `S` is finite.
`(iii)` Let `G` be the set of points on a line. Then `G` is infinite.
`\color{green} ✍️ \color{green} \mathbf(KEY \ POINTS)`
• When we represent a set in the roster form, we write all the elements of the set within braces `{ }.`
• It is not possible to write all the elements of an infinite set within braces `{ }` because the numbers of elements of such a set is not finite.
• So, we represent some infinite set in the roster form by writing a few elements which clearly indicate the structure of the set followed ( or preceded ) by three dots.
`"For example,"` `{1, 2, 3 . . .}` is the set of natural numbers,
` \ \ \ \ \ \ \ \ \ \ \ {1, 3, 5, 7, . . .} ` is the set of odd natural numbers,
` \ \ \ \ \ \ \ \ \ \ \ {. . .,–3, –2, –1, 0,1, 2 ,3, . . .}` is the set of integers. All these sets are infinite.
`\color{green} ✍️ \color{green} \mathbf(KEY \ POINTS)`
• All infinite sets cannot be described in the roster form.
• For example, the set of real numbers cannot be described in this form, because the elements of this set do not follow any particular pattern.
`\color{green} ✍️ \color{green} \mathbf( "Cardinality of a finite set" )`
`"Cardinality"` of a finite Set is defined as total number of elements in a set.