Inequality with floor function exponential

[visual tapir]

Hey guys I'm reading this paper and I'm stuck on this

[waxen meadow]

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[rustic bolt]

what exactly does the first line mean?

is there some n0 for which this ineq holds

i take it q is fixed

[visual tapir]

precisely

[rustic bolt]

but how do we conclude what follows

[visual tapir]

it is

[rustic bolt]

does L have some extra assumption

is it monotone or.. ?

[visual tapir]

what L?

[rustic bolt]

the function

or is that alpha

[visual tapir]

damn my f looks that bad?

but yeah it has some conditions, but the paper doesn't use them

[rustic bolt]

you say n geq n0 implies.. does that mean for all n?

[visual tapir]

just has to be bigger than n0

[visual tapir]

here

tho this n0 has nothing to do with the one in my question

sorry not sharing this before, but the paper just kinda treats this inequality as natural almost

[visual tapir]

the one in my question

[rustic bolt]

the definition defines what it means for a sequence of positive numbers to be C0

[rustic bolt]

is f supposed to be C0 or whats going on here?

[visual tapir]

that's exactly it

[rustic bolt]

Ohh

i get it

you have to prove such an f is C0

[rustic bolt]

so this is true

[visual tapir]

it's assumed it is C0, then the inequality holds, though I suspect this holds for any sequence with the constraints in my question

[rustic bolt]

that could also be, but then we assume f is C0 and show the bound holds

[visual tapir]

yes

[rustic bolt]

should have included the definition right away then

[visual tapir]

you're correct

[rustic bolt]

take log at base q from both sides

[visual tapir]

this then?

i still don't see it

if it weren't for the floor function ...

oh god

I think I see it now

[visual tapir]

this looks alright?

i think it does and we don't even have to assume C0

can't believe I didn't think of putting the goddamn log in there

thanks a lot @rustic bolt

[rustic bolt]

looks good, indeed C0 seems unnecessary, maybe its a general remark about bounding positive sequences

[visual tapir]

seems that way

[rustic bolt]

havent seen the paper, cant say

[visual tapir]

ou of curiosity

here it is

if you wanna have a headache

[rustic bolt]

at work rn, have several already

[visual tapir]

legend

thanks again

[vague dagger]

@visual tapir

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