# All Mathematicians Please come to this thread

#### Arthraxium wrote:

Are we done?
Wow.

The image means 4.00-5.99 if anybody doesn't know
[iimx->4+f(x), limx->5-f(x)] :/
Dont laugh, at least i tried
To clarify, "4*-5*" can be really misleading, because there are two meanings which can be interpreted behind this:

Which means all the beatmaps between 4.0-5.0 star rating

or

Which means the set of all the 4-star beatmaps (beatmaps with 4 as the leading integer), plus all the 5-star beatmaps.

So the solution is to tell those MP basturds to clarify what they mean with the title.
Or just make a room and don't rotate host. Therefore the title will always be right for you.
I don't multi, so I'm all gud.

#### Arthraxium wrote:

I don't multi, so I'm all gud.

#### Arthraxium wrote:

I don't multi, so I'm all gud.
Good idea. I will follow your example.
CE + dont buy supporter = perfect excuse to not go into multi

#### B1rd wrote:

There is a very complicated mathematical and philosophical problem that needs to be solved.

That is, does 4-5*, as in the context of the title for a multiplayer lobby mean 4.0-5.0*, or 4.0-5.99*, or something else entirely?

This needs to be solved once and for all. Let the debate begin.
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.

#### Arthraxium wrote:

.
If only there was a way to put this equation in the lobby name.
it actually means 5-6

(but what is 5-6??)

#### Arthraxium wrote:

Are we done?
We are most certainly not done. You haven't even defined f(x)! As near as I can tell, you intend for f(x) to be a many-valued function that takes on as values all maps with star ratings equal to the argument. From there, we have to define some sort of ordering on the set of maps in order to make sense of the interval. I guess the obvious choice is to consider all maps of the same star rating to be members of an equivalence class and then using the standard total order on real numbers over the star rating associated with each equivalence class.

However, I'm not entirely sure that this is what you meant because it raises some questions about your choice of notation. For one thing, I wonder why you would have chosen to use f(x) as boundaries of your interval, rather than choosing an interval for x and then indicating that we were accepting all f(x) for all x in that interval. It also makes me wonder why you used the limits, when you could, assuming I had correctly interpreted your notation, just as easily have chosen f(4) to be the lower limit and f(6) to be the upper limit. Your choice to use limits makes me think there must be some sort of discontinuity at x=4 and x=6 and it's not clear to me what would cause that to happen. Even more baffling is your choice to use one-sided limits. I honestly have no idea what quantity you could have had in mind that would have different limits from the left and the right that would make sense in the context in which you used them.

When we've sorted all of that out, we can get back to the very important argument taking place in this thread over trivial details.
wtf
From what I've learned in Statistics class: If you have a range of 4 to 5, it will have boundaries that reach from 3.5 to 5.5. This would be a different story if the lobby were titled 4.0-5.0 (in which case the boundary would be 3.95-5.05), or even 4.00-5.00 (where the boundary is 3.995-5.005 and thus effectively ceases to matter unless you bother calculating the floating point values of each difficulty). Therefore, the game is mathematically correct in how it categorizes the difficulty ratings... people just need to start making better lobby titles.
Are you seriously trying to say people's usage of a star rating number should be measured with a confidence interval or something
No, I'm just saying that people should use more decimals.

#### YayMii wrote:

No, I'm just saying that people should use more decimals.
Yes.
The convention YayMii is referring to comes from using significant figures. However, since star ratings are given to the nearest hundredth (and likely calculated to include significant figures beyond that), using significant figures to justify that convention is just silly. If someone means 3.5-5.5, they can simply say so. The relevant mathematical convention here would be that 4-5 means everything in the interval [4,5], where the square brackets indicate that the endpoints of the interval are included. Expecting people to all use that specific meaning is kind of ridiculous though.
Is any of this really relevant? I mean most of us dont play multi and if we do its with friends so why care?
If you dont play with friends shame on you
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 won't really have anything 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.