If I’m understanding correctly, the argument here is:
A)
B)
C)
Therefore, .
First off, this seems to have an implicit assumption that .
I think this assumption is true for any functions f and g, but I’ve learned not to always trust my intuitions when it comes to limits and infinity; can anyone else confirm this is true?
Second, A seems to depend on the relative sizes of the infinities, so to speak. If j and k are large but finite numbers, then if and only if j is substantially greater than k; if k is close to or larger than j, it becomes much less than or greater than −1/12.
I’m not sure exactly how this works when it comes to infinities—does the infinity on the sum have to be larger than the infinity on the limit for this to hold? I’m pretty sure what I just said was nonsense; is there a non-nonsensical version?
In conclusion, I don’t know how infinities work and hope someone else does.
...why did someone promote this to a Frontpage post.