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I don't think maths even play a role in this topic lol since we're not using proper mathematical annotations in the first place
Here I can do non-notation tooN0thingSpecial wrote:
I don't think maths even play a role in this topic lol since we're not using proper mathematical annotations in the first place
4* maps --> All maps that have at least 4 stars and no more than 4.99
5* maps --> All maps that have at least 5 stars and no more than 5.99
4*-5* maps -> 4.00 to 5.99
"4-5" stars as a multi title
Ambiguous since the person reading might assume 4.00 to 5.00 or all 4 star and all 5 star maps.
Solution:
USE BETTER MULTI LOBBY TITLES YOU FUCKS
Suddenly this topic is popular. I guess everyone is a mathematician
Every single compiler of every relevant programming language ever truncates when casting floating point to integers and doesn't round. (Also, this is the exact reason why I too think that 4-5* means 4.0 to 5.99.)Endaris wrote:
@Khelly: So you are some fucking compiler that is too stupid to round numbers when converting to integer. gg
Khelly is right.
Or they use the definition by the difficulty-grouping and think it is 3.5-5.5
Wait let me ask a friend who is actually studying maths as a degree
Endaris wrote:
Or they use the definition by the difficulty-grouping and think it is 3.5-5.5
I never liked that rounding system to begin with. As an example, can you agree that I have a 7 star fc because of my #1 play because it's 6.8*? I don't.
4*-5* maps -> 4.00 to 4.99You don't exclude last number in stack. Same as you cannot exclude first number from it.
[4* - 5*] = {4.00, 4.01, 4.02, ... , 4.98, 4.99, 5.00}
I mistyped there 5.99 as 4.99 then I changed it to 5.00 because you confused me.[Taiga] wrote:
4*-5* maps -> 4.00 to 4.99You don't exclude last number in stack. Same as you cannot exclude first number from it.
[4* - 5* ] = {4.00, 4.01, 4.02, ... , 4.98, 4.99, 5.00}
xdB1rd wrote:
There is a very complicated mathematical and philosophical problem that needs to be solved.
from a philosophical view it's 3.5 - 5.5 because that what 4* and 5* taps have
Consider calculating the arithmetic mean of 4 and 5 as the sup and inf of our setArthraxium wrote:
Are we done?
Then take the integral from 4 to 5 over the sinus of our arithmetic mean multiplied with pi.
Wow.Arthraxium wrote:
Are we done?
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
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.
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.
Arthraxium wrote:
I don't multi, so I'm all gud.
Good idea. I will follow your example.Arthraxium wrote:
I don't multi, so I'm all gud.
CE + dont buy supporter = perfect excuse to not go into multi
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.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.
If only there was a way to put this equation in the lobby name.Arthraxium wrote:
.
it actually means 5-6
(but what is 5-6??)
(but what is 5-6??)
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.Arthraxium wrote:
Are we done?
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.
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.
Yes.YayMii wrote:
No, I'm just saying that people should use more decimals.
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 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.
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.
I think you're misunderstanding the point of significant figures.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.
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.
No, if we are speaking purely mathematically it means:YayMii wrote:
If we're speaking strictly mathematically.
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.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.
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