Is the convergence of an infinite series mere convention?

[jbriggs444]

Even though it is an infinitely long sum, and at what ever finite level you look, there is always another "3".

It is a convention to call this a "sum", and in many ways it acts like one, but it is not an infinitely long sum. Instead it is the limit of the sequence of partial sums.

 

[pat8126]

Where is this from?
"Is this simply because infinite series are *defined* by their converged limit even though they only become infinitesimally close to it?"

That was from a previous posting that I deleted. It was starting to explore the philosophy of mathematics so I removed it accordingly.