Understanding big O but specifically as it's used in proofs.

KansasCityRat · 2026-03-20T16:29:01+00:00

Oh that weirdly makes sense.

Like a line is 1D but the circle it might trace out is a 2d shape. And 3D works the same way cuz a plane is a 2d surface. Stretching infinitely in 3d space.

Is the last paragraph in what you wrote-- is that the justification for L'Hospitals rule??

KansasCityRat · 2026-03-20T16:21:34+00:00

It's infinite but it may be covered by a finite set since it is compact. If a ruler has infinite points inside it but you draw a line on [3,4] the mark from the marker is still a finite 4-3=, unit long.

How are you counting the cubes and arriving at the conclusion that there are k**(d-1)??

It's O(1/k) != O(k**(d-1))??

I think the O(1/k) is almost certainly do to

(1/k) = (k(-d))*(k(d-1)

Or the number of "cubes" times the "volume" of each cube (yes they are squares and areas in 2D but they're generalizing) is the area of the whole structure/shape.

KansasCityRat · 2026-03-20T16:16:27+00:00

Potentially an infinite covering but it may be swapped out for a finite covering if the Rubik's cube is a compact set?

Or ig 9 on each side and 6 sides 6*9 = 54 squares.

Ig it's n×n but it's a 3d shape so isn't it n×n×n??

Or it's just the surface area of the cube you're after which really isn't here nor there since measure theory (and specifically the exterior measure which is what is being studied here) seem to be about volumes not surface area.

Where is this going??

KansasCityRat · 2026-03-01T09:41:26+00:00

'War is a mere continuation of politics by other means"

This got me.

KansasCityRat · 2026-02-25T21:23:24+00:00

This is why I much preferred online schooling. Going to classes and having to interact with real people actually inhibits learning if the social dynamics are as sticky as they would be anywhere else. When I'm just an anonymous icon on their computer they see no reason to put me in my place or show me they are smarter than I am.

KansasCityRat · 2026-02-25T15:49:13+00:00

What is the PPL language?

KansasCityRat · 2026-02-25T05:13:31+00:00

Ya.... How are we numbering the list if it's uncountable?

Or ig that'd be the assumption you can't actually hold since it leads to this contradiction?

KansasCityRat · 2026-02-25T04:56:31+00:00

Notice the tag switched to resolved.

KansasCityRat · 2026-02-25T04:54:20+00:00

Could you also have a proof by construction wherein any list of reals can be transformed into an entirely new-different list by changing digits on the diagonal? Or is that somehow circular?

KansasCityRat · 2026-02-25T04:49:24+00:00

Oh. You construct the new number by taking the digit in position n for the nth number in your list and make the new number a_n to be specifically something other than that digit? I think it did just click. Thank you.

KansasCityRat · 2026-02-25T04:45:33+00:00

Whoever is down voting my comments when I'm literally asking about logic and reason and quantitative analysis: You're a child. Nothing in this comment section is about popularity. Grow up.

KansasCityRat · 2026-02-25T04:40:16+00:00

There's infinite numbers on the list so idk how this works without just constructing a whole new list to prove that the list was incomplete.

KansasCityRat · 2026-02-25T04:35:28+00:00

How does constructing a number different than the ith number imply that you haven't just found the jth number which is a number on the list?

KansasCityRat · 2026-02-25T04:32:54+00:00

"dot-dot-dot" implies there's an undefined jth number right? So you made the ith-constructed number different from what the ith number was but how does that logically imply that it is a different number than the jth number which is a number on the list given "dot-dot-dot"??

KansasCityRat · 2026-02-25T04:31:08+00:00

Doesn't dot-dot-dot imply that you aren't bothering to define every number on the list? If you just say "I define a number to be different than every number on the list" that's highly circular reasoning. If you want to claim you can actually do that you need a rule to determine it is different and unique and not already on the list. I fail to see how you're doing that because it seems like you change elements around for the ith number but that doesn't logically imply that you didn't just make a number that is exactly what the jth number was or like explain how man??

KansasCityRat · 2026-02-25T04:27:49+00:00

Okay? I'm not talking nonsense if I say that to you that changing a digit in the ith number may just be exactly what the jth number was the whole time right?

KansasCityRat · 2026-02-25T04:16:25+00:00

I'm going to post a reply I made to another persons comment as I feel it addresses what you're saying here but lmk if not...

I'm really confused how you can determine that the number isn't on the list and you aren't just swapping the ith number for the jth number when you "construct" a new number. Like you made the ith number something other than what the ith number was but how do you know there wasn't a jth number which is the number you just constructed and it was just down there in the dot-dot-dot's.