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Old 2020-04-02, 16:06   #20
kriesel's Avatar
Mar 2017
US midwest

31·149 Posts

What the heck, as long as we're throwing out any pretense of following the sort of integer and rational number math the video seems to begin premised upon, let's compare the two series in the original post mod small n. I propose mod 1 to keep things simple. The sum of any series consisting of positive integers mod 1 is zero. Then the two series are equivalent.
Mod 2 could also be a lot of fun, allowing the series to switch positions among >, < and = as the number of terms increases. Schroedinger's cat now has 3 states, and oscillates between them like neutrinos; perhaps awake, asleep, and dead.
Let A = 1 + 1 + 1 + ...
and A(i) = 1, defined for i a positive integer
Let B = 1 + 2 +3 + ...
and B(i) = i, defined for i a positive integer
A mod 2 alternates between 0 and 1 at each term; even+1=odd; odd+1=even.
B mod 2 alternates between 0 and 1 at each two terms. Odd + even = odd; odd + odd = even.

Last fiddled with by kriesel on 2020-04-02 at 16:11
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