1-1. We
discussed how a concept is created by our mind. It abstracts the similarity from several things in order to group them. In mathematics we call these concepts SET. Dog
is a concept for the animals with particular similarities, in mathematics dog
is defined as a set of animals which have those common properties.
Set is one
of the basic concepts which cannot be defined; however almost everybody can
understand it. Set
of mathematicians, set of bicycles, set of psychological disorders, and set of
smiles.
Members
or elements are things that belong to a set. Gauss is a member of mathematicians,
but Lionel Messi is not one of its elements. Since we use this format
frequently that a particular member is an element of a particular set,
we replace “is an Element of” with this symbol ∈ (stretched E). So translated into math
language, we write Gauss ∈ mathematicians. We could even simplify it
more, if we used Gauss and mathematicians frequently. Therefore, we could write
that G ∈ m (In the context G and m must be defined). “Messi
is not an element of mathematicians” can be simplified as M ∉ m. You can see how a sentence can be written
in mathematical language more simply and easily.
Like the words in English that we memorize for communication, we should keep in mind the
symbols in order to read them correctly, otherwise they look like some weird,
mysterious or even terrifying codes.
If we change the arrangement such that we say "mathematicians" consists the element named Gauss, we write it m ∋ G, or m ∌ M (for mathematicians which doesn't have an element called Messi). Most of the times we use the first arrangement " the member is (or is not) an element of the set".
