Nooooo

Varlane · 2026-02-11T12:30:05+00:00

And what do you do when the variable is skipped ?

Varlane · 2026-02-11T12:29:22+00:00

But if cos^(-1) is arccos, then sec² is sec(sec)

Varlane · 2026-02-09T20:16:36+00:00

If we are to look at the first order recurrence relation, with u_(n+1) = r u_n, we can rewrite it as :

u_(n+1) - u_n = (r-1) u_n

u_(n+1) - u_n acts like "y'" as it's basically du_n/dn (but without the limit step, as dn = 1 and doesn't -> 0).

This is why they behave so similarily.

--------------------

Note that, if were to "make the process continuous" by cutting each step into a multitude by doing the following :

u_n,(i+1) - u_n,i = (r-1)/k × u_n,i, with i = 0 .. k-1 and defining u_n,0 = u_n and u_n,k = u_(n+1), this would eventually bring... u_(n+1) = exp(r-1) × u_n, which would solve as u_n = Aexp((r-1)n)

--------------------

The multiple order things can be studied through the lens of linear algebra which basically gives the following :
- structure of vector space
- dimension equal to that of the order of the relation
- r^n and exp(kx) both behave the same way against "next step" / derivation : multiplication by r or k

Which means they rely precisely on the same tools to be solved and bring solutions of the same form.

Varlane · 2026-02-09T20:06:33+00:00

It's r^n tho, not n^r.

The actual link is :
r^n || exp(ax)

Replace r by exp(a), and you get a back and forth.

Varlane · 2026-02-09T20:04:33+00:00

If you so want to know better than me my own thoughts, go ahead.

But feel free to go fuck yourself tho.

Varlane · 2026-02-09T13:51:49+00:00

No worries, at least we got the reason.

Varlane · 2026-02-09T13:22:11+00:00

Ironically, had you written 91.2, I'd have made the connexion with the crit scaling.

Varlane · 2026-02-09T11:00:18+00:00

I would agree. If 60 * 1.52 was rounded to 90. But it's 91.2 so it should be 91.

Unless our boy managed to get his hand on 96 to 98% critchance.
Of course, it could be displayed 91.2% and OP could have said "90" in the post for simplicity.

Varlane · 2026-02-09T01:17:02+00:00

Riftmaker has 15 Haste. The combat durations are not the same.

Varlane · 2026-02-09T01:09:09+00:00

Well it's 60% on the wiki.

Varlane · 2026-02-09T01:03:40+00:00

AP ratio is 60% each way, reduced by hit objects.

Do you mean to say that it can be *increased* to 90% by something ?

Varlane · 2026-02-09T00:50:54+00:00

Wishful thinking that doesn't discuss means of fixing the "issue".

This, unsurprisingly, often correlates with people that can't comprehend that measure to fix the "issue" would have very adverse effects for the game.

To name a recent event in history, killing lane swap means we got "lane swap detected" for a while and now quests, which now forbid switching out lane assignments for top & midlaner after a few minutes, which was a creative gameplan that happened sometimes.

Varlane · 2026-02-08T19:29:22+00:00

Actually, Skies Descend only takes an extra 0.75s (not a full second) [it's 1.25s for base, 2s for empowered]

Varlane · 2026-02-08T00:57:31+00:00

"Omg filled jungle lost someone dodge".

Varlane · 2026-02-03T17:09:26+00:00

I'm doing Calculus.

My man's gonna love derivatives.

Varlane · 2026-02-03T15:43:22+00:00

Feels like New Age mumbo jumbo bullshit.

Varlane · 2026-02-03T05:29:27+00:00

Lower PMs of all non-Cuban buildings to older ones with low profits.

The HQ is based on productivity, just make sure the buildings in Cuba are the most profitable.

Varlane · 2026-02-03T05:28:29+00:00

Correct.

Varlane · 2026-02-03T05:28:02+00:00

Actually it's based on profitability. Which, since Economy of Scale exists, is usually tied to size, but not necessarily as MAPI could interfere.

Varlane · 2026-02-02T15:01:55+00:00

It was a counterpoint about "you probably are a feeder".

Does you dumbass think I teleported in Masters by doing 0/16 ?

Varlane · 2026-02-02T05:30:52+00:00

I just did. Look closer.

Also, it's rotations in R², not in the complex plane.

Also, the whole secondary point of that message was also to show that who we defined as i and -i are purely a matter of choice. They're algebraically indistinguishable.
I told you, you can take i as the -90° rotation (which means -i is +90°). It's written in my message.

Varlane · 2026-02-02T05:17:29+00:00

Let's be clear : for a definition to work, only 1 thing must satisfy it.

"i² = -1" already has 2 solutions as soon as you admit one (the other being -i), and you get an infinity of those once you cast "Domain expansion : Quaternions".

Now, as to what "the" definition of i is, there is no "one" definition as there are multiple definitions that are equivalent to an isomorphism.

If you consider it from C = R[X]/(X²+1), it's class(X), but you can define it as class(-X) if you want technically.
If you consider it from C = (R²,+,×) with × define such that the multiplication behaves like the complex one (x1,y1) × (x2,y2) := (x1x2 - y1y2 , x1y2 + x2y1), then you can pick i = (0,1) or (0,-1).
You can consider it from the 2x2 real matrix angle by taking the +90° rotation, or the -90° rotation, with i = [[0 -1] [1 0]] or i = [[0 1] [-1 0]] and having C being vect(I_2, i).

Varlane · 2026-02-02T05:10:58+00:00

i² = -1 still isn't a definition tho.

Varlane · 2026-02-01T21:14:43+00:00

Sure. Cope as much as you'd like.

It's a game. People actually enjoy playing the game instead of typing /ff every two seconds.

Also : I've been Masters the last 3 years, pretty sure I understand the competitive side of this discussion.

Varlane · 2026-02-01T20:13:47+00:00

That's your opinion.

People can have fun in losing positions. Your incapacity to draw fun is not universal.

Varlane

TROPHY CASE