Can A or B be finite if A cross B is not the empty set?

[physicsuser]

sets A and B. A cross B not equals the empty set. Prove that A or B is finite.

I think that you can't... don't ask me for my work because I have none.

 

[Townsend]

I think that you can't

I agree.

The regular x,y coordinate system is a cross product of real numbers. Each ordered pair is an element of the cross product and it is not the empty set and yet set A = set B and set A is not finite.

 

[physicsuser]

If anyone thinks that it can be proved, then just say that it can be and give me a hint in the right direction please.

Thanks for peeking in.

 

[Townsend]

If anyone thinks that it can be proved, then just say that it can be and give me a hint in the right direction please.

Thanks for peeking in.

I thought I just gave you a counter example. Your statement is basically a universally quantified statement for sets, unless I am reading it wrong, and so just a single counter example is sufficient to prove that it is not true. You cannot prove something is true if it is not true. I am not a expert on set theory but in this case it seems pretty straight foreword, no?

Best of luck...

 

[physicsuser]

I thought I just gave you a counter example. Your statement is basically a universally quantified statement for sets, unless I am reading it wrong, and so just a single counter example is sufficient to prove that it is not true. You cannot prove something is true if it is not true. I am not a expert on set theory but in this case it seems pretty straight foreword, no?

Best of luck...

Sorry, but I am a total noob with sets. I see it as, if they ask you to prove something then it must be true; atleast it was true for all the other question.

As for this question I think that there is not enough info to conclude anything about A or B besides that none of them is an empty set. I've reread the set section and there is nothing about what makes a set finite(I do know what a finite set is).

 

[Townsend]

Sorry, but I am a total noob with sets. I see it as, if they ask you to prove something then it must be true; atleast it was true for all the other question.

As for this question I think that there is not enough info to conclude anything about A or B besides that none of them is an empty set. I've reread the set section and there is nothing about what makes a set finite(I do know what a finite set is).

If the question said

A cross B is not the empty set, prove that there exist at least one case where set A or set B is finite, then you could but prove there is at least one case by showing one example. No problem

A={x,y} and B={r,s}

So A cross B is just

{(x,r),(x,s),(y,r),(y,s)}

QED.

But your question asked in us to prove this is true for all sets A and B. How can you prove something that is not true?

I think you must have the question wrong because it really does not make much sense. I bet it asked to prove that if A or B is finite then A cross B is finite. Maybe you could look at the question one more time and make sure you got it right.

Best of luck