Kuratowski's definition of an ordered pair $(a,b)$ to be the set given by $\bigl\{\{a\},\{a,b\}\bigr\}$ achieves this objective, in that the defined object has precisely the property we want an "ordered-pair-whatever-it-may-actually-be" to have. Choose to substitute in for to find the ordered pair. Determine which ordered pair represents a solution to a graph or equation. Definition (ordered pair): An ordered pair is a pair of objects with an order associated with them. The first set of ordered pairs is a function, because no two ordered pairs have the same first coordinates with different second coordinates. It is a subset of the Cartesian product. Subtract from . Write as an equation. Algebra. Example 5.3.10 Since the partial orderings of examples 5.3.1, 5.3.2 and 5.3.3 are not total orderings, they are not well orderings. Multiply by . Or simply, a bunch of points (ordered pairs). Step-by-Step Examples. Use the and values to form the ordered pair. A function is a set of ordered pairs such as {(0, 1) , (5, 22), (11, 9)}. If you're seeing this message, it means we're having trouble loading external resources on our website. An ordered-pair number is a pair of numbers that go together. Two ordered pairs (a, b) and (c, d) are equal if and only if a = c and b = d. For example the ordered pair (1, 2) is not equal to the ordered pair … If objects are represented by x and y, then we write the ordered pair as (x, y). Simplify . Example: {(-2, 1), (4, 3), (7, -3)}, usually written in set notation form with curly brackets. https://www.khanacademy.org/.../cc-6th-coordinate-plane/v/plot-ordered-pairs Since there is no smallest integer, rational number or real number, $\Z$, $\Q$ and $\R$ are not well ordered. A relation or a function is a set of ordered pairs. The set of all first coordinates of the ordered pairs is the domain of the relation or function. Functions. The numbers are written within a set of parentheses and separated by a comma. Remove parentheses. Like a relation , a function has a domain and range made up of the x and y values of ordered pairs . Determine which ordered pair represents a solution to a graph or equation. Ordered-Pair Numbers. In other words, the relation between the two sets is defined as the collection of the ordered pair, in which the ordered pair is formed by the object from each set. a) Prove that {{x}, {x,y}} = {{u}, {u,v}} if and only if x = u and y = v. Therefore, although we know that (x,y) does not equal {x,y} , we can define the ordered pair (x,y) as the set {{x}, {x,y}}. Find Three Ordered Pair Solutions. b) Show by an example that we cannot define the ordered triple (x, y, z) as the set {{x}, {x,y}, {x,y,z}} 2. For example, (4, 7) is an ordered-pair number; the order is designated by the first element 4 and the second element 7. Answer Since this set has that property, we define that set to be what the ordered pair "really is". The set of all second coordinates of the ordered pairs is the range of the relation or function.

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