More on Sequences

Fun class activity:

1. Let $A = \langle 1, 2, \dots, 10\rangle$.
   1. How much is $\sum_{j \in A} j$?
   2. How much is $\prod_{m = 1}^5 a_m$?
2. Let $B = \langle 4, -4, 3, -3, \,$$2, -2, 1, -1, 0\rangle$.
   1. How much is $\sum_{b \in B} b$?
   2. How much is $\prod_{m = 1}^{|B|} p_m$?

We use size ($|B|$) and element inclusion ($j \in A$) notation for sequences, too. However, there is a difference between sets and sequences in terms of size: $|\{1, 1, 1, 1\}| = 1$ because we just repeat the same set element, while $|\langle1, 1, 1, 1\rangle| = 4$ since every term has a unique position in the sequence and is, therefore, meaningful (it isn't just repetition.)