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Math and science::Analysis::Tao::07. Series
Summation over finite sets, definition
Let \( X \) be a set with \( n \in \mathbb{N} \) elements and let \( f: X \rightarrow \mathbb{N} \) be a function from \( X \) to the real numbers. Then we define the finite sum \( \sum_{x \in X} f(x) \) as follows.
Select any [...] \( g \) from \( \{i \in \mathbb{N} : 1 \le i \le n \} \) to \( X \). Such a [...] exists since \( X \) is assumed to have \( n \) elements. We then define:
\[ \sum_{x \in X} f(x) := \sum_{i=1}^{n}[...] \]
