Asklemmy

43415 readers

1555 users here now

A loosely moderated place to ask open-ended questions

Search asklemmy 🔍

If your post meets the following criteria, it's welcome here!

Open-ended question
Not offensive: at this point, we do not have the bandwidth to moderate overtly political discussions. Assume best intent and be excellent to each other.
Not regarding using or support for Lemmy: context, see the list of support communities and tools for finding communities below
Not ad nauseam inducing: please make sure it is a question that would be new to most members
An actual topic of discussion

Looking for support?

Looking for a community?

Lemmyverse: community search
sub.rehab: maps old subreddits to fediverse options, marks official as such
[email protected]: a community for finding communities

~Icon~ ~by~ ~@Double_[email protected]~

founded 5 years ago

MODERATORS

[email protected]

118

What is your favorite paradox or conundrum? I am partial to can god kill god? (lemmy.world)

submitted 5 months ago* (last edited 5 months ago) by [email protected] to c/[email protected]

291 comments fedilink hide all child comments

The monotheistic all powerful one.

you are viewing a single comment's thread
view the rest of the comments

[–] [email protected] 9 points 5 months ago (2 children)

So the resolution lies in the secret that a decreasing trend up to infinity adds up to a finite value. This is well explained by Gabriel's horn area and volume paradox: https://www.youtube.com/watch?v=yZOi9HH5ueU

[–] [email protected] 3 points 5 months ago (1 children)

If I remember my series analysis math classes correctly: technically, summing a decreasing trend up to infinity will give you a finite value if and only if the trend decreases faster than the function/curve x -> 1/x.

[–] [email protected] 2 points 5 months ago (1 children)

Great. Can you give me example of decreasing trend slower than that function curve?, where summation doesn't give finite value? A simple example please, I am not math scholar.

[–] [email protected] 1 points 5 months ago* (last edited 5 months ago) (1 children)

So, for starters, any exponentiation "greater than 1" is a valid candidate, in the sense that 1/(n^2), 1/(n^3), etc will all give a finite sum over infinite values of n.

From that, inverting the exponentiation "rule" gives us the "simple" examples you are looking for: 1/√n, 1/√(√n), etc.

Knowing that √n = n^(1/2), and so that 1/√n can be written as 1/(n^(1/2)), might help make these examples more obvious.

[–] [email protected] 1 points 5 months ago (1 children)

Hang on, that's not a decreasing trend. 1/√4 is not smaller, but larger than 1/4...?

[–] [email protected] 1 points 5 months ago

From 1/√3 to 1/√4 is less of a decrease than from 1/3 to 1/4, just as from 1/3 to 1/4 is less of a decrease than from 1/(3²) to 1/(4²).

The curve here is not mapping 1/4 -> 1/√4, but rather 4 -> 1/√4 (and 3 -> 1/√3, and so on).

[–] [email protected] 2 points 5 months ago

Here is an alternative Piped link(s):

https://www.piped.video/watch?v=yZOi9HH5ueU

Piped is a privacy-respecting open-source alternative frontend to YouTube.

I'm open-source; check me out at GitHub.