a
this post was submitted on 29 Sep 2023
549 points (100.0% liked)
196
17963 readers
461 users here now
Be sure to follow the rule before you head out.
Rule: You must post before you leave.
Other rules
Behavior rules:
- No bigotry (transphobia, racism, etc…)
- No genocide denial
- No support for authoritarian behaviour (incl. Tankies)
- No namecalling
- Accounts from lemmygrad.ml, threads.net, or hexbear.net are held to higher standards
- Other things seen as cleary bad
Posting rules:
- No AI generated content (DALL-E etc…)
- No advertisements
- No gore / violence
- Mutual aid posts are not allowed
NSFW: NSFW content is permitted but it must be tagged and have content warnings. Anything that doesn't adhere to this will be removed. Content warnings should be added like: [penis], [explicit description of sex]. Non-sexualized breasts of any gender are not considered inappropriate and therefore do not need to be blurred/tagged.
If you have any questions, feel free to contact us on our matrix channel or email.
Other 196's:
founded 2 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
What is ∞ + ∞?
Let x_n be an infinite, real sequence with lim(n -> ∞) x_n = ∞.
Let y_n be another infinite, real sequence with lim(n -> ∞) y_n = ∞.
Let c_n be an infinite sequence, with c_n = 0 for all n ∈ ℕ.
Since y_n diverges towards infinity, there must exist an n_0 ∈ ℕ such that for all n ≥ n_0 : y_n ≥ c_n. (If it didn't exist, y_n wouldn't diverge to infinity since we could find an infinite subsequence of y_n which contains only values less than zero.)
Therefore:
lim(n -> ∞) x_n + y_n ≥ lim (n -> ∞) x_n + c_n = lim(n -> ∞) x_n + 0 = ∞
□
i think this means that ∞ + ∞ > ∞
Not quite. It's somewhat annoying to work with infinities, since they're not numbers. Technically speaking, ∞ + ∞ is asking the question: What is the result of adding any two infinite (real) sequences, both of which approaching infinity? My "proof" has shown: the result is greater than any one of the sequences by themselves -> therefore adding both sequences produces a new sequence, which also diverges to infinity. For example:
The series a_n = n diverges to infinity. a_1 = 1, a_2 = 2, a_1000 = 1000.
Therefore, lim(n -> a_n) = ∞
But a_n = 0.5n + 0.5n.
And lim(n -> ∞) 0.5n = ∞
So is lim(n -> ∞) a_n = 2 • lim(n -> ∞) 0.5n = 2 • ∞?
It doesn't make sense to treat this differently than ∞, does it?
Sounds like the infinite hotel paradox
Here is an alternative Piped link(s):
Sounds like the infinite hotel paradox
Piped is a privacy-respecting open-source alternative frontend to YouTube.
I'm open-source; check me out at GitHub.
Wait, isn't there some thought experiment where you can insert infinity into infinity simply by moving infinity over by one infinite times?
I'm too lazy to look it up rn
Yup, someone else commented it in this thread.
https://sh.itjust.works/comment/3777415