Simple question, please help

  • Thread starter sniffer
  • Start date
112
0
ehm, sorry, i am a beginner in set theory. learning on my own.
for cartesian product ordered pair, for example
[itex] A = \{a_1, a_{2}, a_{3}\} \\
B = \{b_{1}, b_{2}, b_{3}\} [/itex]

is the product [itex] A \times B = \{a_{1}b{1}, a_{1}b{2}, a_{1}b{3}, a_{2}b{1}, \\
a_{2}b{2}, a_{2}b{3}, a_{3}b{1}, a_{3}b{2}, a_{3}b{3},\} [/itex] ??

What does [itex] A \times B = \{(a,b)\mid a \in A and b \in B\} [/itex] mean in detail?

thanks.
 
112
0
sorry, a bit mistyped the question above.

for cartesian product ordered pair, for example
[itex] A = \{a_1, a_2, a_3\} [/itex] and [itex]B = \{b_1, b_2, b_3\} [/itex]

is the product [itex] A \times B = \{a_{1}b{1}, a_{1}b{2}, a_{1}b{3}, a_{2}b{1}, \\
a_{2}b{2}, a_{2}b{3}, a_{3}b{1}, a_{3}b{2}, a_{3}b{3},\} [/itex] ??

What does [itex] A \times B = \{(a,b)\mid a \in A \ and \ b \in B\} [/itex] mean in detail
in terms of individual set member for this simple example?

thanks.
 

matt grime

Science Advisor
Homework Helper
9,392
3
the elements in the product are the pairs (a_i,b_j) for 1<= i,j <=3.

what does a_1b_1 even mean?

the product is all odered pairs (a,b) where a is in A and b is in B. nothing more nothing less.
 
112
0
[itex] a_i [/itex] and [itex] b_i [/itex] are numbers or element such as 1, 6, 8, etc.

i think i may understand your simple answer.

thanks
 

matt grime

Science Advisor
Homework Helper
9,392
3
the product of sets does not involve multiplying the elements; elements of sets do not necessarily even possess a multiplicationwhat if A were the set of results of drawing a card and B were the set of results of tossing a coin? if a were the three of diamonds and b heads, then what does ab mean?
 

HallsofIvy

Science Advisor
41,620
821
Notice the parentheses in [itex] A \times B = \{(a,b)\mid a \in A \ and \ b \in B\} [/itex]?

What you want is
[itex] A \times B = \{(a_{1},b{1}), (a_{1},b_{2}), (a_{1},b_3}), (a_{2},b_{1}), (a_{2},b_{2}),\\ (a_{2},b_{3}), (a_{3},b_{1}), (a_{3},b_{2}),(a_{3},b_{3}),\}[/itex]
 
Last edited by a moderator:
112
0
yup. now i understand it. thanks guys.
 

Want to reply to this thread?

"Simple question, please help" You must log in or register to reply here.

Related Threads for: Simple question, please help

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top