Today's counter-intuitive fact is brought to you by the Natural Logarithm.pic.twitter.com/lphAcxseQ4
PhD student of Theoretical Particle Physics @UCIrvine l @NSF Fellow l Physics & Math Animations l Patreon: https://www.patreon.com/inertialobserver …
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Today's counter-intuitive fact is brought to you by the Natural Logarithm.pic.twitter.com/lphAcxseQ4
Here's my direct proof for the equality.pic.twitter.com/RDm6MqqwTD
Because two infinite series converge to the same number can we equate them? What are we exactly equating? The convergence or the infinite series?
The Infinite series, but of course they must also both then converge
Honestly I have trouble with this equating from a logic perspective. The equal operator holds only at infinity. Everywhere else they are not equal.
It’s just a regular equality between two infinite sums
OK then, does the infinite sum determines the equality or the process that leads to infinite sum?
It says that the sums converge arbitrarily close to the same number for sufficiently large N
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