Lesson 2: Using i,j
I have a question about using i and j in partitions and labeling. The textbook uses the definitions 1<=i, j<=n, but I am a bit confused as to why this is so since (if I'm not mistaken) i and j are in the same set? For example, on page 16, {{pi, pj}: 1<=i, j<=99 and i=/=j}. My question is, why not {{pi,pj}: 1<=i<=99, 1<=j<=99 and i=/=j} (similar to how i is defined in set A)? (Sorry for the confusing formatting/notation, I don't know how to do that here.) If someone could explain to me, that would be great! Thanks in advance!
weisbart: Jan. 12, 2015, 7:41 a.m.
I see what you're saying, this is just a simple notation issue. The notation \[1\leq i,j\leq 99\] actually means \[1\leq i\leq 99 \quad {\rm and}\quad 1\leq j\leq 99.\] It's just a compressed way of writing it. So, you're right in how you want to describe the set.
AshleyChang: Jan. 12, 2015, 12:06 p.m.
Oh wow, I completely did not see that. I thought they were individual....Thank you!