I am doing IGCSE Maths, and am having a few problems with function notation. I understand the form f(x)
.
What does the form f: x ↦ y
mean? Could you also give one or two examples?
And, if possible, state your source. Thank you.
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Sign up to join this communityI am doing IGCSE Maths, and am having a few problems with function notation. I understand the form f(x)
.
What does the form f: x ↦ y
mean? Could you also give one or two examples?
And, if possible, state your source. Thank you.
It means that $f$ is a function that takes the value $x$ to the value $y$. For instance, $$f: x\mapsto x^2$$ is an alternate way of writing $f(x) = x^2$.
$f:x \mapsto y$ means that $f$ is a function which takes in a value $x$ and gives out $y$.
But,
$f: \mathbb{N} \to \mathbb{N}$ means that $f$ is a function which takes a natural number as domain and results in a natural number as the result.
\to
and \mapsto
respectively.
$\endgroup$
As it is evident from math.stackexchange notation — the symbol $\mapsto$ reads as "maps to".
This is backed up by Wikipedia article on functions:
... the notation $\mapsto$ ("maps to", an arrow with a bar at its tail) ...
There is another arrow-symbol, which also used for mapping $\rightarrow$, which might be a bit confusing. The difference between two (as it is mentioned in the linked answer, as well as in the answer by MathEnthusiast):
Example (borrowed from here):
$$f:R \rightarrow R$$ $$x \mapsto x^2$$
It means that: under $f$, any element $x \subset R$ gets mapped to the element $x∗x=x^2$ (which is also an element of $R$).