12 Questions
What is the condition for two ordered pairs (a,b) and (a',b') to be equal?
a=a' and b=b'
What is the main difference between the sets {a,b} and {b,a} and the ordered pairs (a,b) and (b,a)?
The order of elements
What is the term used to describe an ordered collection of n elements?
n-dimensional vector
What is the geometric interpretation of an n-dimensional vector when n=2?
A point on the plane
What is the condition for two n-dimensional vectors (a_1,a_2,a_3,...,a_n) and (a'_1,a'_2,a'_3,...,a'_n) to be equal?
a_1=a'_1, a_2=a'_2, a_3=a'_3,..., a_n=a'_n
What is the minimum number of sets required to form a Cartesian product?
2
What is the Cartesian product of sets A and B denoted by?
A×B
In the Cartesian product of sets, what is important about the order of elements in pairs?
The order is important
What is the Cartesian product of n sets denoted by?
∏_(i=1)^n▒A_i
What is the special case of the Cartesian product of sets A_1, A_2, A_3,..., A_n, when all sets are equal?
The n-th Cartesian power of set A
What is the 2nd Cartesian power of set A also called?
The Cartesian square of A
What is the result of the Cartesian product of sets A, B, and C, when A={x,y}, B={10,20}, and C={%, $}?
={(x,10,%),(x,10,$),(x,20,%),(x,20,$),(y,10,%),(y,10,$),(y,20,%),(y,20,$)}
Learn about the definition of Cartesian product of sets, including the concept of ordered pairs and how they differ from identical sets. Understand the properties of ordered pairs and how they are generalized to any number of ordered elements.
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