My message on discrete stclairdrake.netematics explains:
A relation is a subset of a Cartesian product and also a function is a special type of relation.
You are watching: A relation is a special type of function
But it would certainly make much more sense come me if a role described a relation together a subset the the Cartesian product.
My think being:Given a function, f(x) = y, we have the right to compute a set of (x,y) collaborates within the Cartesian plain. And this set of works with would be the relation the is the subset that the Cartesian product.
Am i confused? could anyone help explain just how a role IS a relation?
features discrete-stclairdrake.netematics relationships
request Sep 8 "16 at 5:19
23322 silver- badges66 bronze title
include a comment |
4 answers 4
active earliest Votes
A duty is a certain kind the relation.
The best means to understand this is v the assist of an example. So, let us take a pair of to adjust - set $A$ = 1, 2, 3 and collection $B$ = $a$, $b$, $c$. Hence the set $A \times B$ will have 9 elements.
We can select $2^9 = 512$ different subsets of $A \times B$. Every of this subset is a relation between $A$ and $B$. So, $\phi$ is a relation, $(1, a), (1, c), (2, b)$ is additionally a relation. $A$ is referred to as the domain and also $B$ is dubbed the co-domain.
A duty is also a subset the $A \times B$ (hence a relation), yet it has actually constraints. For every element in collection $A$, there have to be precisely one aspect in set $B$. An ext concretely, for every aspect $x$ in set A, there is exactly one $(x, y)$ in $f$ for some $y \epsilon B$
For example, $(1, a), (2, b), (3, b)$ is a function, yet $(1, a), (2, b)$ is not because there is no entry of the form (3, *). Also, $(1, a), (1, b), (3, b), (2, b)$ is likewise not a duty because 1 has actually two values it is mapping to.
edited Sep 8 "16 in ~ 6:37
answer Sep 8 "16 at 5:38
Pratyush RathorePratyush Rathore
33111 silver badge55 bronze title
add a comment |
A duty is a binary relation where the an initial value that the pair is unique.
If $A$ and $B$ are sets, then a binary relationship $R$ is just a collection of bag $(a,b) \in A \times B$. A function is a special type of relation where given any kind of $a \in A$ there is just one $b \in B$ such the $(a,b)$ is $R$. That is, both $(a,b_1)$ and also $(a,b_2)$ cannot be in $R$ unless $b_1 = b_2$.
See more: The Principal Culture That Transferred Greek Astronomical Knowledge To Renaissance Europe Was:
For a function $f : A \to B$, we deserve to express $f$ as the collection of facets $(a,b) \in A \times B$ wherein $b = f(a)$. In collection builder notation,
$$f = \(a,f(a)) : a \in A,\ f(a) \in B\.$$
Since any type of subset the $A \times B$ is a relation from $A$ come $B$, a role is certainly a relation.
edited Sep 8 "16 at 5:45
reply Sep 8 "16 at 5:36
Alexis OlsonAlexis Olson
5,1861515 silver- badges3232 bronze title
add a comment |
Think the the relationship "is much less than" in $\1,2,3\^2$. That relation is $\stclairdrake.netrmLess=\(1,2),(1,3),(2,3)\$, however you normally will not write $(x,y)\in\stclairdrake.netrmLess$, however you will write $x
authorize up making use of Facebook
Post as a guest
Not the prize you're looking for? Browse various other questions tagged features discrete-stclairdrake.netematics relationships or questioning your very own question.
stack Exchange Network
expropriate all cookie Customize settings