Set Notations – Maths Lesson

Set Notations and stuff to remember:

Why remember? Remembering is boring. We don’t believe in memorising things.

But some things are necessary to remember because the whole world of maths uses them as we discussed in the last article.

Do not go after directly memorising things. Your brain is a powerful computer and if you solve enough problems related to the chapter or concept, you will automatically remember such trivial things like how to represent a set in Set-Builder form.

Solve questions on Set Theory by visiting

  • Sets are denoted by capital letters of English alphabet like $A, B, C,$ etc.
  • The internal elements of the set (or members, or objects) are denoted by small letters of English alphabet like $a, b, c, d,$ etc.
  • $\in$ is another important symbol used as a shortcut (called epsilon from Greek symbol). Put simply, if you want to say that if some element belongs to some set, then you use this symbol. For example,

$a \in S$ says in a shortcut that element $a$ belongs to set $S$.

Pause for a moment and think how this notation saves time if you are working with lots of set problems.


If you want to say some element “does not belong to” a set, then you use the symbol $\notin$.

$4 \notin Y$

letter $a \in E$ where E is the set of all letters in English alphabet

but $\Delta \notin E$

Pause and think about this for a minute. Think of 5 more examples from different areas of life where you can denote of some object/member belongs in some set or not.

  • The order in which you write the elements in a set is not important. So:

{1, 2, 3, 4, 5} is the same as writing {5, 4, 3, 2, 1} or {4, 3, 5, 1, 2}

{a, b, c, d} is same as {c, a, b, d}

  • If you want to write a really, really long set or an infinite set in Roster form, you can use a shortcut again (isn’t math filled with shortcuts?).

{1, 2, 3, 4, 5, …} says that this set goes on forever. (Set of all Natural numbers)

  • If you are writing some set in Roster form again, you don’t need to repeat the elements you write in them. i.e each element is only written once.

{1, 1, 1, 1, 1} is unnecessary. The correct set is {1}.

  • All the elements inside a set share some common property. That is why they are all in that set. You cannot exclude some element that has the common property from some set. And you cannot include some element that does not have the common property with other elements.

For a set of all even numbers greater than $0$ and less than $10$, we cannot write {2, 4, 8, 9}. You must include $6$ in this set. And you cannot include $9$ in this set as it does not share the common property of being an even number.

Nothing fancy right? Do not memorise any of the above stuff. Instead, solve lots of problems related to sets.

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