Re: Mathematics with the potential infinite - some inexhaustible?
martdowd at aol.com
martdowd at aol.com
Sun Feb 5 11:37:50 EST 2023
Dennis Hamilton writes:
Now it is certainly a fair point that obtaining zero as the limit as n goes to infinity of 2^-n is the limit of an infinite sequence. What is bothering me is the idea that because the sequence is infinite, it is therefore not something we can experience.
This is true of mathematical objects in general. An integer n can be "experienced" in everyday life in various ways. But what about Z_n, the ring of integers mod n? Also, infinity can be experienced in some ways. A line segment in 3-dimensional Euclidean space has uncountably many points. Everyday life example of countably infinite sets seem more involved.
Martin Dowd
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