Recent content by brookey86

I can see that i will always be less than n+1. But is there a way to compare the two without using the product summation symbol?

Homework Statement n! < (n+1)n I am not looking for a proof, just a way to simplify this equation mathematically. Homework Equations The Attempt at a Solution As far as I can see, I cannot simplify this any further. Is there something I can divide out of both sides, for example?

No, I think #2 would still be antisymmetric and transitive

With the way I wrote it no. But I actually made a typo, it should be w+x <= y+z AND w<=y. So I'd say yes

Homework Statement Are these two relations reflexive, antisymmetric, transitive? 1. (w,x)<=(y,z) iff w+x <= y+z 2. (w,x)<=(y,z) iff w+x <= y+z AND w<y Homework Equations The Attempt at a Solution 1. reflexive - yes; antisymmetric - no; transitive - yes; 2. reflexive -...

Thank you for the help. I couldn't find any online texts that explained relations where uncertainty was involved.

So it seems I'm correct with my reasoning above, except perhaps for asymmetric because x drawing y doesn't necessarily imply that y did not draw x.

Our text uses the latter.

So am I on the right track?

Homework Statement The relation xRy is defined as "x has drawn a picture of y". R is on the set of all people. Is this relation: reflexive, irreflexive, symmetric, asymmetric, antisymmetric, transitive ? Homework Equations What confuses me about this problem is that there is uncertainty...

Homework Statement For each positive int k, there are k consecutive pos ints that aren't perfect-squares. I'm trying to write this in symbolic logic, but am getting messed in the second part and might be a little off on the first. Homework Equations The Attempt at a Solution...

I can prove it using words, not quite there using mathematical symbols, but that part is out of the scope of my class. Thanks guys!

Homework Statement Homework Equations The Attempt at a Solution