Dear Doron,
Let me tell you that your abstract is even bound with problems... Let's dissect it, shall we?
A and B are sets.
q and p are numbers of R (the set of all real numbers).
No problem here. Maybe you should add "suppose" and change the second assumption so it becomes:
suppose A and B are sets.
suppose q and p are real numbers.
Now here lies the first problem:
Option 1: q and p are members of A , but then q is not equal to p .
By saying "option 1", do you mean "case 1"?
Btw let me tell you that you didn't mention anywhere that p is not equal q, so
we cannot say "then q is not equal to p".
Let me give you an example.
suppose q and p are real numbers.[/color]
Now, q and p can both be 7, can't they (because there are no restrictions). Which means if a set A contains p, then A contains q. That means...
q and p are members of A[/color]
Which is case 1. But they are not different! So we CANNOT conclude that
but then q is not equal to p[/color]
You should address this problem before we continue the rest. You MAY have a great and revolutionary idea (which, I'm so sorry to say that I doubt), but you need to present it in a stepwise logical manner.
Did you mean:
suppose q and p are real numbers
, with p not equal q.
Please reply
Thank you