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## Main Question or Discussion Point

First, I would like to clear up notation and the definition for sequences. What exactly is a sequence? I read somewhere that it is defined as a function ##f: \mathbb{N} \to \mathbb{R}##. But if this is the case, why do we only define functions based on the range of the function, e.g., ##\left \{ 1, 4, 9, 16... \right \}## (which we regard as "the sequence")? We define sequences with the notation ##\left \{ a_{n} \right \}_{0}^{\infty}## too, but what does this mean in terms of the functions concept? How does this specify a function? In addition, what is the nth term's relation to the function concept, or in other words, what is the analogue of the nth term for sequences in functions? Finally, what exactly to the terms "partial sums, series, finite series, infinite series," mean? It seems as though they are mostly for the same concept.