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Set
A collection of objects. Each object in the set is called an element (or member) of the set.
We usually name sets with capital letters (such as $A$, $B$, $C$) and write their elements inside curly brackets $\{\ \}$.
Element
The simplest form of matter that cannot be broken down into simpler substances by physical or chemical means.
To talk about membership we use:
If $A=\{16,25,36,49,64\}$ then $49\in A$ but $81\notin A$.
The cardinality of a set $A$ is the number of elements it contains, written $n(A)$.
Cardinality
The cardinality of a set $A$, written $n(A)$, is the number of elements in $A$.
If $A=\{\text{knife, fork, spoon}\}$ then $n(A)=3$.
You will commonly meet three descriptions of the same set:
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Paywall
(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.
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