A method of listing the elements in a row with comma separation within curly brackets is called the roster notation.

The roster notation is a simple mathematical representation of a set in mathematical form.

In this method, the elements (or members) are enumerated in a row inside the curly brackets. If the set contains more than one element, then every two elements are separated by a comma symbol.

Due to the listing of elements one after one, the roster method is also called the enumeration notation.

In set $A$, there is only one element. Hence, the element $3$ is displayed within curly brackets.

$A \,=\, \Big\{3\Big\}$

In sets $B$ and $C$, we have more than one member. Hence, the members are listed one after one between curly brackets with comma separation.

$B \,=\, \Big\{1, 2, 5, 6, 8, 9\Big\}$

$C \,=\, \Big\{x, y, z\Big\}$

This mathematical form is called the roster form or enumeration form.

The roster method is very simple method for representing a set in mathematical form but it has some limitations.

The roster notation is not comfortable to express many elements in roster form.

$D \,=\, \Big\{1,$ $2,$ $3,$ $4,$ $5,$ $6,$ $7,$ $8,$ $9,$ $10,$ $11,$ $12,$ $13,$ $14,$ $15,$ $16,$ $17,$ $18,$ $19,$ $20\Big\}$

$E \,=\, \Big\{a,$ $b,$ $c,$ $d,$ $e,$ $f,$ $g,$ $h,$ $i,$ $j,$ $k,$ $l,$ $m,$ $n,$ $o,$ $p,$ $q,$ $r,$ $s,$ $t,$ $u,$ $v,$ $w,$ $x,$ $y,$ $z\Big\}$

The set $D$ expresses the roster form of the numbers from $1$ to $20$. Similarly, the set $E$ expresses the roster form of alphabets from $a$ to $z$.

The two sets are lengthy and it is not convenient for writing such sets in roster form. Just imagine the roster form of a set if the set contains more than $100$ elements. It becomes a nightmare for everyone to write it. However, some sets follow a pattern or have a particular sequence.

In order to overcome this issue, the first three or four members along with a continuous symbol and last element are written between the curly braces.

$D \,=\, \Big\{1, 2, 3, \ldots, 20\Big\}$

$E \,=\, \Big\{a, b, c, d, \ldots, z\Big\}$

Some sets have infinite elements. It is not actually possible to express all of them in roster form. Similarly, we donâ€™t know the last element in these types of sets. If sets follow a pattern or have a particular sequence, we just write the first three or four elements with a continuous symbol within the curly braces.

The set $F$ represents the odd numbers in natural numbers.

$F \,=\, \Big\{1, 3, 5, \ldots \Big\}$

$F \,=\, \Big\{1, 3, 5, 7, \ldots \Big\}$

The actual problem comes to the roster method with repeated elements in the set. If the elements are few, we can easily express the set in roster form as follows.

$G$ $\,=\,$ $\Big\{0,$ $1,$ $2,$ $3,$ $2,$ $5,$ $0,$ $9$ $\Big\}$

If the set contains many elements with repeated elements, it is either uncomfortable or impossible to express the elements in roster notation because the elements do not follow a pattern or have a particular sequence. In this case only, the roster notation is not recommendable in set theory.

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