YayMii wrote:

If we're speaking strictly mathematically, the star ratings are categorized by 1 significant digit, displayed to the hundredths (or 3 sigdigs for the majority of maps), and calculated at a floating point value. If only one digit is given in the lobby title, it should be mathematically safe to assume that anything within the class boundaries would be acceptable (given that this is how the game categorizes them anyways).
That being said, the limits of an actual lobby have absolutely nothing to do with mathematics, simply due to the fact that some people are more lenient than others when it comes to what they are willing to play although a lot people disapprove of my map choices regardless of difficulty lolrip.

I think you're misunderstanding the point of significant figures.

Suppose you have a meter stick that's subdivided into centimeters. Further suppose that these centimeters are not subdivided into millimeters, but that markings have been made halfway between each consecutive pair of centimeter markings. If you use this meter stick and find that an object is between 33.5 and 34 cm long, you can round this result and say that the object is 34cm long. This measurement would have 2 significant figures. When performing calculations with this number, you would report the result of the calculations using a number of significant figures that's determined according to specific rules. These specific rules prevent rounding errors accumulated along the way from finding their way into the final answer.

I think it's safe to assume that the numbers used by the difficulty calculator have enough decimal places and enough significant figures that star ratings could be given to more than 2 decimal places without suffering from rounding errors accumulated along the way and they can certainly be given accurately to 2 decimal places. Including 3.5 when saying "4" isn't a matter of caring about significant figures, as this would be implying a degree of uncertainty that does not actually exist in the numbers used. The type of uncertainty that does exist in star ratings comes rather from algorithm imperfections, which very much do not respect mathematical rules of rounding or significant figures. A specific 5.6 star map may very well be easier for the average player than a specific 4.9 star map, for example, and a player may consider both of these to be de facto 5 star maps.

Some people do use "4-5" to mean "3.5 - 5.5", but in most cases, I would expect this to stem either from not wanting to use decimals (which makes the notation ambiguous) or from following the conventions the game uses when sorting maps by star rating. Using this convention on the basis of significant figures is simply not correct.

Even if they put a 3 star or a 6 star, I'll still play them so it's not like it matters too much. That's how multi worked when those "3.5-4.5*" "4-5*" "4-6*" memes were still not used.

Just to clarify, I'm not talking about solely significant figures. I'm talking about class boundaries in relation to significant figures. The game divides the difficulty categories this way, hence why I brought it up.

Finally, we have a real mathematician here. I'm just a plain old soon-to-be-physicist.

for the problem of this magnitude, I think we need actual scientists here.

YayMii wrote:

If we're speaking strictly mathematically.

No, if we are speaking purely mathematically it means:

chainpullz wrote:

4-5 typically translates to [4,5] \in \R unless you say "4-5 exclusive" in which case it translates to (4,5). So no, anything >5 would not be included.

FFS people, OP didn't ask for a scientist or programmer, they asked for a mathematician. I seriously question everybody's backgrounds here as I doubt any of you actually qualify as a mathematician.

4-5 is quite literally shorthand for "from 4 to 5" which is a way of specifying two endpoints of an interval. In no rigorous mathematical world is anything less than 4 or greater than 5 contained within this interval. We aren't speaking computer number systems, we aren't speaking whatever fucked up statistics or science rounding systems have taught you. We are speaking pure theoretical rigorous math.

Sincerely,
Irritated Pure Mathematician

P.S. https://xkcd.com/435/ there's a reason why we stay way the fuck away from all of you people

4-5 now means 4 and 5 instead of 4 to 5

B1rd wrote:

4.0-5.0*, or 4.0-5.99*, or something else entirely?

It is 4.00 to 5.00 type "star>=4 star<=5". But 5.49* is acceptable coz it can be rounded to 5 using standard rules any higher is considered 6 star just consult with lobby first.

Where is mathexpert when we need him?

oh god khelly you created a monster

Someone ask https://osu.ppy.sh/u/Cirno - she made perfect math class so will know for sure

I think the root of the problem is how osu! sorts beatmaps from x.5-X.5. Why wasn't it sorted from x.01 to X.99?

[Taiga] wrote:

Someone ask https://osu.ppy.sh/u/Cirno - she made perfect math class so will know for sure

At least Cirno can count better than Microsoft, amirite?

The Gambler wrote:

I think the root of the problem is how osu! sorts beatmaps from x.5-X.5. Why wasn't it sorted from x.01 to X.99?

That has nothing to do with math. That's purely an implementation choice. Last time I checked Peppy is a software developer and not a Mathematician...

The notation 4-5* has got absolutely nothing to do with math either.
why is this still going, someone make a poll

chainpullz wrote:

P.S. https://xkcd.com/435/ there's a reason why we stay way the fuck away from all of you people

If all mathematicians are this snotty, it's a wonder anyone would want to be near them at all!

GhostFrog wrote:

chainpullz wrote:

P.S. https://xkcd.com/435/ there's a reason why we stay way the fuck away from all of you people

If all mathematicians are this snotty, it's a wonder anyone would want to be near them at all!

I think you'd be offended too if everyone and their grandmother pretended to be an expert on your subject and spouted off nonsense about it all the time. It's like programmers calling themselves software "engineers." If bridges, nuclear reactors, space shuttles, cars, air planes, chemical plants, etc. failed with the same frequency that software did half of us would probably be dead by now. Real engineers don't justify catastrophic failure with "oh, we'll fix that in the next patch," they get it right the first fucking time.

chainpullz wrote:

I think you'd be offended too if everyone and their grandmother pretended to be an expert on your subject and spouted off nonsense about it all the time. It's like programmers calling themselves software "engineers." If bridges, nuclear reactors, space shuttles, cars, air planes, chemical plants, etc. failed with the same frequency that software did half of us would probably be dead by now. Real engineers don't justify catastrophic failure with "oh, we'll fix that in the next patch," they get it right the first fucking time.

#notruescotsman

Did anyone in this thread pretend to be an expert on math? This was clearly not actually meant to be a thread specifically for mathematicians and it should come as no surprise that lots of non-mathematicians came to the thread to argue silly mathematical interpretations. Perhaps a more suitable response to this thread would have been to calmly explain the actual mathematical side of things.

I do have to wonder though...you seem pretty sure that "my subject" isn't math. What gives you this impression?

just don't pick newbie maps and everything will be good

GhostFrog wrote:

chainpullz wrote:

I think you'd be offended too if everyone and their grandmother pretended to be an expert on your subject and spouted off nonsense about it all the time. It's like programmers calling themselves software "engineers." If bridges, nuclear reactors, space shuttles, cars, air planes, chemical plants, etc. failed with the same frequency that software did half of us would probably be dead by now. Real engineers don't justify catastrophic failure with "oh, we'll fix that in the next patch," they get it right the first fucking time.

#notruescotsman

Did anyone in this thread pretend to be an expert on math? This was clearly not actually meant to be a thread specifically for mathematicians and it should come as no surprise that lots of non-mathematicians came to the thread to argue silly mathematical interpretations. Perhaps a more suitable response to this thread would have been to calmly explain the actual mathematical side of things.

I do have to wonder though...you seem pretty sure that "my subject" isn't math. What gives you this impression?

Of all the other people in this thread you are actually the most likely candidate for actually knowing what you are talking about judging only on what you wrote.. I deliberately left that statement out knowing that the average G&R reader would misconstrue it as agreeing with someone who shares the same view as opposed to agreeing with someone who shares the correct view.

The Gambler wrote:

I think the root of the problem is how osu! sorts beatmaps from x.5-X.5. Why wasn't it sorted from x.01 to X.99?

It's actually X.49 to (X+1).49


Get it right

Endaris wrote:

4.0-5.0 with an optional margin of tolerance of like 0.25.

4-5* is a range
4* and 5* are values

The way I see it

The way I see it, you're talking about 4 stars TO 5 stars
So 4.0-5.0 imho

If you say specifically 5 stars, then you probably mean AROUND 5 stars, which could be, idk, 4.8-5.2 or something, unless you specify exactly 5 stars

Different people have different opinions about this subject so

DeathAdderz wrote:

just make a room and don't rotate host. Therefore the title will always be right for you.

or don't multi at all.

Case closed

4* isn't a value to me, it's all maps that have at least 4 whole stars but not more than 5


4.0 is a value to me

4 and 4.0 are actually the same thing. Even with an asterisk.

DeathAdderz wrote:

or don't multi at all.

Case closed

hai hai

Mahogany wrote:

If you say specifically 5 stars, then you probably mean AROUND 5 stars, which could be, idk, 4.8-5.2 or something, unless you specify exactly 5 stars

"5 stars" is ambiguous as it is either short hand for "maps in a 5 star \delta neighborhood," "maps of at least 5 stars," or simply it's literal meaning of "5 stars."

Maps in a 5 star \delta neighborhood: B_{\delta}(x) = {y \in \R | (x-\delta) <= y <= (x+\delta)}. In this case \delta is usually taken to be .5 so that the neighborhoods form a partition on \R.

Maps of at least 5 stars: {y \in \R | y >= 5}

5 star maps: {5}

The issue is that using either of the first two interpretations makes no sense in the context of endpoints of an interval which is why "5*" is ambiguous but "4*-5*" is not.

B1rd wrote:

4 and 4.0 are actually the same thing. Even with an asterisk.

Only tangentially related to your comment but the integer 4 , the rational number 4, the real number 4, etc. are all set theoretically different. This isn't an issue here because 4 and 4.0 are both valid ways of expressing the same four (WoLoG assuming 4.0 has meaning).

B1rd wrote:

4 and 4.0 are actually the same thing. Even with an asterisk.

No. With an asterisk 4* means to me "4 star maps" not " a four point 0 star map"

3.50-5.49 I'd say

The only difference between Khelly's inclusion of all fractions and the usual rounding is that he places the entire 0.99999... star error on one side instead of evenly distributing it. It doesn't make it more correct that the resulting range starts with the number it was derived from, it just has more potential to be annoying (in multiplayer, or wherever else)

I think 4.0-5.0 is the correct one, but it doesn't matter much because the addition of a flexible margin of error would make it practical instead.

Why can't you think of an average 4 star map as 4.5 stars then? With easy 4 star maps being like 4.2 or some shit and hard ones being 4.8, 4.9

Khelly wrote:

Why can't you think of an average 4 star map as 4.5 stars then? With easy 4 star maps being like 4.2 or some shit and hard ones being 4.8, 4.9

Because they are all values intermediate to 4 and 5 hehe

Momiji wrote:

Khelly wrote:

Why can't you think of an average 4 star map as 4.5 stars then? With easy 4 star maps being like 4.2 or some shit and hard ones being 4.8, 4.9

Because they are all values intermediate to 4 and 5 hehe

This is no problem to me because to me a 4 star map must have 4 full stars but no more than 5. I SAID THIS ALREADY

chainpullz wrote:

"5 stars" is ambiguous as it is either short hand for "maps in a 5 star \delta neighborhood," "maps of at least 5 stars," or simply it's literal meaning of "5 stars."

Maps in a 5 star \delta neighborhood: B_{\delta}(x) = {y \in \R | (x-\delta) <= y <= (x+\delta)}. In this case \delta is usually taken to be .5 so that the neighborhoods form a partition on \R.

Maps of at least 5 stars: {y \in \R | y >= 5}

5 star maps: {5}.

I have no idea what the fuck you're saying, but in my opinion the problem is people not being specific as to what they're saying, not using words like "around" "higher than" "below" and such which creates such ambiguity that everyone argues over.

True, Khelly, the problem is that 4-5 reads as 4 to 5 which means that it starts at 4 and ends at 5.
Or differently spoken:
if expression = "x to y"
then
x:=limes inferior, lowest boundary
y:=limes superior, highest boundary
with the assumption that both numbers are exact numerical values (because it doesn't make sense to NOT give exact numerical values as you elaborated previously) which equals to either of these intervals:
(4;5)
(4;5]
[4;5)
[4;5]

yeah it's not like i omitted it or anything but i felt like answering specifically for myself xd

what's the difference between a 5 star 5.00 map, 5 star 5.01 map, 5 star 5.99 map, and 5 star 6.01(yes) map?
to be both correct and practical i'd say that all three last ones are wrong, but still go off the idea that what is not constant for them is how mad people will get at me for picking them in a 4-5 star lobby.

which is why there will be no clear boundary for me, I will just gradually feel worse for picking something above like 5.15-5.3 stars
despite being really unrelated to the "math" portion it's really important i think

edit: riince notice me

chainpullz wrote:

FFS people, OP didn't ask for a scientist or programmer, they asked for a mathematician. I seriously question everybody's backgrounds here as I doubt any of you actually qualify as a mathematician.

Who are you calling 'they'? And I was being somewhat ironic with the OP if you didn't notice.

Khelly wrote:

B1rd wrote:

4 and 4.0 are actually the same thing. Even with an asterisk.

No. With an asterisk 4* means to me "4 star maps" not " a four point 0 star map"

4 = 4.0

* stands for stars. It is not a number modifier. It does not change the value of 4 in any way. 4* does not mean 4 to 4.99* any more than 4 apples means 4 to 4.99 apples.

I don't care if green is blue to you, I'm just stating what is. At least, that is my understanding of maths.

And you're not reading 4* as a short hand for "Four stars" or "Four star maps" where "Four star maps" is actually a range of map difficulties?

Endaris wrote:

True, Khelly, the problem is that 4-5 reads as 4 to 5 which means that it starts at 4 and ends at 5.

I'm not talking about 4-5. I'm talking about 4*-5*