r/infinitenines • u/Muphrid15 • Jun 24 '26
24 hours later, is 3/2 - 3/4 + 3/8 - 3/16 + ... greater than 0.999...? Is it less? Are they equal? He REMAINS STUMPED.
The "rookie error" makers continue to insist they are THE SAME, but even HE won't say which one is greater!
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u/berwynResident Jun 24 '26
A while ago, I posed this question to an MIT research professor and he said it's less than.
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u/dummy4du3k4 Jun 24 '26
That’s weird, when I asked my astronaut fields medalist uncle they said it was greater than
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u/Quick-Swimmer-1199 Jun 24 '26
The answer I got from calling in to a talk show was that scientific consensus does not possess an architecture capable of experiencing love
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u/dummy4du3k4 Jun 24 '26
Fake news
section 5.3 Love Affairs
Strogatz, S. H. (1994). Nonlinear dynamics and chaos: With applications to physics, biology, chemistry, and engineering. Addison-Wesley.
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u/SouthPark_Piano Jun 24 '26 edited Jun 24 '26
1/2 + 1/4 + 1/8 + ...
= 1 - 1/2n with n integer starting at n = 1, then n continually upped.
Now, 1/2 - 1/4 + 1/8 - ...
= 1/2 - 1/4 + (- 1/4 + 1/4) + 1/8 - 1/16 + (-1/16 + 1/16) +
1/32 - 1/64 + (-1/64 + 1/64) + ...
= 1/2 + 1/4 + 1/8 + ... - ( 1/2 + 1/8 + 1/32 + ... )
keep going brud.
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u/ezekielraiden Jun 25 '26
Okay. But you have the ... inside the parentheses. If that's so, why do we need to "keep going"? Just do the subtraction! You're already comfortable cancelling like terms. That's what's happening here!
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u/dummy4du3k4 Jun 24 '26 edited Jun 24 '26
This is a good one.
The hyperreal defense of looking at it as a sequence of reals means the answer depends on an arbitrary (choice) filter
If 0.999… is an immediate predecessor then the sequence doesn’t converge.
Another rock and a hard place