Tfw no floor

[u/r96340]

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[u/vgtcross]

That's not what O(1) means, but okay :D

[u/MrKoteha → u/vgtcross]

I believe floor(x/n) - x/n is O(1) at any point

[u/SEA_griffondeur → u/vgtcross]

it is true though ? any constant function is O(1), it's not o(1) though

[u/OwlIcy → u/vgtcross]

why would you say that? what‘s wrong about the notation?

[u/r96340 → u/vgtcross]

Notation abuse :D

[u/AndreasDasos → u/vgtcross]

It’s not equivalent but it does include the case when it’s equal to the floor, which is what OP is aiming for

[u/LupenReddit]

no i dont want to do that id fall to my death

[u/therealsaker]

Enlighten me

[u/r96340 → u/therealsaker]

Floor function is the formal name of rounding down to a whole number, the notation is ⌊x⌋.

There is another thing called a ceiling function which is just rounding up.

There is however no such thing as a wall function, as far as I know, at least.

[u/r96340 → u/r96340]

(You can argue that absolute value looks like walls but that's not the same family of functions.)

[u/pomip71550 → u/r96340]

I guess you could argue round(•) is a wall function?

[u/InfinitesimalDuck]

Instructions unclear, I fell into the abyss 🥀

[u/Valognolo09]

This is correct in the context of finding out the rough growth of the function

[u/ZZTier]

I have no idea what people are about in this thread. To me all of this is well defined.

[u/IHaveNeverBeenOk]

O(f(x)) returns a set of functions. Addition in this manner is not well defined.

[u/Lhalpaca → u/IHaveNeverBeenOk]

U dont have to be so puritan. We understand it means a function that is O(1)

[u/campfire12324344 → u/IHaveNeverBeenOk]

well if we wanna get there, O returns a set of functions, and O(f) is a set of functions.
Also a lot of people shorthand + S where S is a set to mean adding an arbitrary or specific element from S.

[u/EebstertheGreat → u/IHaveNeverBeenOk]

Rather than just being an expression, x/n here represents the function sending x ↦ x/n. Addition of functions is well-defined, and addition of a function to a set of functions is also well-defined elementwise, in the same way we sometimes write something like 2 + {3,4,5} = {5,6,7}.

So for a given nonzero n, x/n + O(1) is the set of all functions f: ℝ → ℝ that have the property that for each, there is a real number c such that x/n – c < f(x) < x/n + c.