Is the convergence of an infinite series mere convention?

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The forum discussion centers on the concept of convergence in mathematics, particularly in relation to Zeno's paradox and the implications of infinity. Participants assert that convergence is a well-defined mathematical principle, independent of physical reality, and that it does not imply the existence of a smallest constituent part of reality. The conversation highlights the distinction between finite and infinite sums, concluding that convergence serves as a convention rather than a definitive representation of reality.

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  • #31
votingmachine said:
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.
 
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  • #32
lurflurf said:
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.
 

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