Why does 0.5 round to 1?

[Anonymous No.15832173]

Why does [math]0.5[/math] round to [math]1[/math]?

Equivalently, [math]0.4\overline{999}[/math] rounds to [math]1[/math], right?

What is the smallest number that rounds down to [math]0[/math] instead of rounding to [math]1[/math]?

[Anonymous No.15832177]

>>15832173
*largest

[Anonymous No.15832187]

.5 rounding to 1 is simply convention. If you are asking what is the largest number less than .5 in the reals, the conventional answer would be that it does not exist.

[Anonymous No.15832195]

>>15832187
but why is that the convention? did like, the Royal Society get together in 1680 and decide they were all "glass half full" people or something? i don't understand why that convention exists.

it also seems to break the "symmetry" of the reals when rounding since [math]-0.5[/math] also typically rounds to [math]-1[/math], which means if anyone is unlucky enough to be doing statistics where their data has a non-negligible set of datapoints that equal (to whatever precision of their apparatus or to their computing precision) to 0.5 or -0.5 this skews their statistics to be non-zero in both directions. this would lead me to believe that mathematics' use of this convention biases any statistical sciences toward non-zero results

[Anonymous No.15832212]

>>15832195
If I had to guess its because rounding up at .5, generally will overestimate things, in general most fields like to overestimate rather than underestimate. There is likely no philosophical or mathematical reason why. If you like you could read this page:
https://en.wikipedia.org/wiki/Rounding#History

In terms of statistics, the statisticians could simply not round at .5 then, or use another digit of precision. You are correct that arbitrarily rounding at .5 could produce problems, but because it is arbitrary we can simply not do it.

[Anonymous No.15832222]

>>15832195
You are wrong.
Follow me here.
0 1 2 3 4
5 6 7 8 9

[Anonymous No.15832230]

>>15832212
>You are correct that arbitrarily rounding at .5 could produce problems, but because it is arbitrary we can simply not do it.
why not change rounding to either alternate deterministically which way it is rounded, or to round based on a probability distribution which assigns it to 0 one half of the time and assigns it to 1 the other half of the time? for teaching students in class you could make them alternate 0 or 1 for the former method or provide them a coin to flip for the latter method.

removing a systematic bias that exists in statistics through all scientific/medical/engineering fields seems worth it to me right?

[Anonymous No.15832234]

>>15832222
Follow me here
1 2 3 4 5
6 7 8 9 10

[Anonymous No.15832238]

>>15832230
Its probably not needed I guess. If it had an advantage maybe they would use that method?

[Anonymous No.15832239]

>>15832234
Exactly, equal partition doesn't change.

[Anonymous No.15832270]

>>15832195
>but why is that the convention?
Because it means that you can round a number simply by looking at its first nonsignificant digit, which is convenient.

>it also seems to break the "symmetry" of the reals when rounding since −0.5 also typically rounds to −1,
Yeah, for the same reason.

[Anonymous No.15832342]

>>15832173
All of you miss one crucial fact. Rounding down if the digit is <0,4> and up if it is <5,9> is just a convention, no different from convention that we write + inbetween the number rather than at the front (which is the way polish notation works). Which could be questioned. Why do we write 5+9 and not +(5,9) if in everyday speech we'd say "add 5 and 9"? It's an arbitrary choice that might work better than other conventions for certain applications (pen&paper math) while polish notation works better for computers or writing math papers on a machine rather than in LaTeX.

In any meaningful context there is never a question how to round a number because it's specified, and creating uncertain cases is similar to "trick" math social media questions where the problem lies in the interpretation of notation - I will answer those if I know exactly what are they asking! And it is not true that 0.5 round up to 1, because it depends on the context. In scientific context when taking measurements you round the value to the measurement uncertainty: values measured with a ruler with lines denoting 0.5cm increments should be rounded to the closest line => a real lenght of 19.6cm would be measured as 19.5cm, or when measuring liquid volume with a graduated cylinder that has a scale with 0.2ml increments real volume of 10.3ml would be measured as either 10.2ml or 10.4ml, depending on what and why you are measuring, since when preparing a reaction you have to account for dead volume left on the walls of measuring apparatus you'd rather measure 10.4ml when 10.3 are needed, and some other case might require you to underestimate the real value

[Anonymous No.15832353]

>>15832342
>10.3ml would be measured as either 10.2ml or 10.4ml, depending on what and why you are measuring, since when preparing a reaction you have to account for dead volume left on the walls of measuring apparatus you'd rather measure 10.4ml when 10.3 are needed
this is very interesting. you are arguing that instead of adhering to some rigid convention, rounding should be chosen (in any cases of ambiguity) on the basis of the experimenter's expertise in how the experiment works.

i think that is legitimate. it may lead to bias, but the bias in this case would be an individual's personal bias and not a systematic built into the system due to biased conventions built into the underlying mathematics.

if that were how we operated, it would be much easier to disentangle whether a result was biased or not because we'd know exactly how each player in the game manipulated his or her rounding errors in whatever direction

[Anonymous No.15832412]

Because
down
.0
.1
.2
.3
.4

count: 5

up:
0.5
.6
.7
.8
.9

[Anonymous No.15832451]

>>15832353
>this is very interesting. you are arguing that instead of adhering to some rigid convention, rounding should be chosen (in any cases of ambiguity) on the basis of the experimenter's expertise in how the experiment works.

There is a very rigid convention - metrology is its own science - you always round to the measurement uncertainity, and depending on the nature of the measurement you round either up or down or to the closest value, and always provide the uncertainity, because a measurement is meaningless without uncertainity; By the way of measurement you place the real value within bounds: 13cm +-1mm for example. Agreed upon convention should be applied by everyone, since only in that way can we compare the results obtained by different people. I just wanted to show you that the problem is not purely a mathematical arbitrary choice and that 0.5 isn't always rounded to 1

[Anonymous No.15832460]

>>15832222
Based digits and based digits

[Anonymous No.15832653]

>>15832451
I have never seen or heard this. Last I did any physics, like first year uni, we were taught to just use the jacobian times the estimated standard deviation at the measuring point

[Anonymous No.15833412]

>>15832653
Literary the first lecture of introductory physics by W. Lewin is "measurements are meaningless without uncertainty"

[Anonymous No.15833564]

>>15832173
0.4999999 is not equal to 0.5

Proof of that is flawed and bullshit.

[Anonymous No.15833717]

>>15832173
Because there are 10 numbers which goes into 2 groups exactly
0,1,2,3,4 and 5,6,7,8,9
>>15832234
>>15832412
oh i was late

[Anonymous No.15833723]

>>15832173
Significant figures

[Anonymous No.15834283]

>>15832234
>>15832412
>>15833717
That is retard logic, because you don't round 0 (or 10) at all, as dropping a zero from the decimals does not alter accuracy. It's more like:
1 2 3 4
5
6 7 8 9
So 5 is in the middle, and as such rounding it either way is arbitrary. This is not a huge mystery, and it has been well discussed in history

[Anonymous No.15834338]

>>15834283
this anon makes a very valid point.

[Anonymous No.15834376]

>>15832173
0.5 rounds to 1 by convention. it could round either way, but to keep it consistent, the definition of rounding pushes it up.
according to my 1st year math teacher.

[Anonymous No.15834386]

>>15834376
did your 1st year math teacher explain to you why he or she was pushing an obviously biased method onto you? or did the bias just justify itself by fiat?

[Anonymous No.15834651]

anything less than 0.5 rounds to 0, including 0.49, 0.499, 0.4999, 0.49999, etc.

[Anonymous No.15834659]

>>15834651
except for [math]0.4\overline{999}[/math]

[Anonymous No.15834662]

I've got a related dumb question. Let's say I have 0.34249 and I want to round it to the 3rd decimal. Is it 0.342 because the next number is 4 or 0.343 because the next number is 4 but 4 is rounded up to 5 because of 9 after?

[Anonymous No.15834736]

>>15834283
0 isn't a value tho
1 bird in hand is worth 2 in the bushes
0 bird is worth 0

[Anonymous No.15834785]

>>15832173
What would you prefer it to round to? Zero?
Here. We'll go back to grade school. Let's say you have half of an apple. 0.5 of 1 apple. How much food do you have, roughly? Well, more or less, you have ONE unit of food despite it being HALF of an apple. It wouldn't be ZERO units of food, obviously you have MORE than that. Zero units of food would be a problem, 0.5 units of food is good enough to be called 1 unit.
Another example. Let's say your dick is 0.5 inches tall. Now, how big is your dick - roughly? It wouldn't be ZERO inches tall, that'd make you a dickless eunuch. So obviously you more or less have 1 inch. Rounding up.

That's why. You can be more pedantic than this, but this is why.

[Anonymous No.15834792]

>>15834785
OK, so if you are going to rent an apartment and it only has the first half floor and not a ceiling then that counts as an apartment? or if you want to buy a car but it only has the front two wheels and no back half that counts as a car? or you want a shirt but it only covers your front side, that counts as a shirt?

[Anonymous No.15834801]

>>15834792
A shitty place to live is still a place to live. A car with two wheels is still a car. If I sawed you in half, you'd still be a human being - half or whole.
And really, we already have protocols for some of the weirder examples. Like let's say you had .01 meters. Is that 1 meter? No, it's 1 centimeter. We redefine what "1" means instead of rounding to zero, because that makes no sense whatsoever.

[Anonymous No.15834836]

>>15834792
What is 1x1
What is 1x2
What is 0x2