Bankers Rounding
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Rounding always jackes somebody.
You cannot get away from this fact.
My example is right.
Your judgement is bad.
Who told you "got jacked out of a penny"?
Why you decided 4.79 is exactly 4.79, not 4.791, 4.793 or 4.799?
They just don't have a device and space on price tag to display 3rd digit.
Scales turn to 4.79 on 4.79(0) and stay there until you reach 4.80(0).
So, half of 4.79(?) is 2.39[5(0)-9(9)]. Right rounding is the one which brings less inacuracy. And traditional rounding is definitely the one.
P.S. Will you ditch BR if you'll buy Pistachios for 4.79 per pound and Cashews for 4.59 per pound?
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Code for TallyGenerator -
Once again:
David's conclusions are based on false assumption.
His statement about 200 numbers which are not rounded is insane. Sorry.
Every number went to orunding function, so every number was rounded.
No matter how many zeros you put after 1.0 it does not mean that next, not displayed number must be zero.
Moreover, as I wrote above, appearance of 1.0(0) is statistically impossible. So, we should not take it into consideration.
Knowing that we may say that number 1.000 was rounded down: 1.000[0-9..] > 1.0000.
After that it's clear: BR rounded 10200 numbers down and 9800 numbers up.
Not really accurate.
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Code for TallyGenerator -
Okay, 2.0 rounded to the nearest integer: round(2.0, 0) = 2. Did it round up or down? You could argue either direction. The fact is it is already rounded. Take the following list:
Initial Number Round(x, 0) ABS(Difference)
1.0 1.0 0
1.1 1.0 .1
1.2 1.0 .2
1.3 1.0 .3
1.4 1.0 .4
1.5 2.0 .5
1.6 2.0 .4
1.7 2.0 .3
1.8 2.0 .2
1.9 2.0 .1
2.0 2.0 0
Did 1.0 round up or down? Neither. Did 2.0 round up or down? Neither.
Your logic is flawed, and so is your proof.
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Okay, it's getting fun again, but I do have to admit an earlier error on my part.
When I claimed that Sergiy was too smart to actually believe the stuff he was espousing, I was mistaken. I apologize for the error and promise not to make another mistake for a day or two.
So, back up your claims with code, Giordy, to enlighten us all, or continue to be mocked. It's quite simple really, and if you want help writing the code, I'm sure we could get Best to help you out. The only criteria is that it include a large, randomly distributed data sample set, and that it demonstrates that traditional bias has less (or even equal, since I'm nice like that) bias than the convergent rounding function. Piece of cake, no?
Good luck, and when come back, bring pie, and answers.
PS Your test proved you wrong, and no, BR didn't round 10200 down and 9800 up, which you can easily see earlier in this thread. 9900 up, 9900 down, 200 not at all. The other test code I provided was even more fitting, as it was truly randomly distributed, but unfortunately, it showed the exact same results, that you were wrong. Give it a shot Fonzi, it's not that hard to say. W-r-o-n-g.
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Sorry, typed wrong numbers.
BR rounded 10100 numbers down and 9900 numbers up.
Those which you consider not rounded are actually rounded down.
There are no absolutely precise values in this world. Go to school and ask a teacher about that.
Those "precise" numbers you see represent real values between this particular number and next "precise" number in line.
If you'll measure million of values represented by 0.005 with 2 more digits precision you'll find out that average value is around 0.0054(9).
If you see the digits behind the scene - you round up.
But if you don't see it because your "scales" or your "tags" don't have space for it - what does it change? It's still the same value, just not displayed in full.
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Code for TallyGenerator -
Have to repeat again:
1.0 is rounded down.
If you add another digit - what 1.0 would turn to?
1.00? Or 1.05? Or 1.08?
You don't know. Any option.
And 1.0 represents all those options. And 1.00, and 1.05, and 1.08.
So, when you round 1.0 you round possibly 1.03. Or 1.04? Who knows? It's just hidden from you.
And ABS(Difference) you've got with given precision. You see 0.0 - it does not mean it's actually 0.0, it could be anything between 0.0(incl.) and 0.1(excl.). You just don't have space to indicate those numbers.
That's why 1.0 is rounded down with ABS(Difference) < 0.1.
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Code for TallyGenerator -
First, you are wrong. There are 2 types of numbers: rational and irrational. Then number 1/8 is a rational number and is represented precisely as 0.125 (and if you want, you can add as many zeros as you want after 5, it is still 0.125. The number 1/3 is the other, or irrational, type of number as it is represented as .333 (and that goes on for as long as you wish to write a 3).
So, we do have precise numbers, so again, you are wrong.
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What is precision of your "1" and "8"?
There are no precise numbers.
Every so called precise number is just a representation of a range of values between this number and the next one in line.
This world is continuous.
Discrete "precise" numbers reflect real values inaccurately.
This is fact of life.
You just missed this chapter from schoolbook.
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Code for TallyGenerator -
Okay, I stand corrected, both 1/8 and 1/3 are rational numbers as these fractions are represented as a ratio of two integers. Irrational numbers are real numbers that cannot be representes a ratio of two integers, such as the square root of 3 or pi.
The range of numbers may be infinite, but the numbers themselves can be precise. If you have 8 apples in a basket, you have 8 apples in a basket, not 8.1 or 7.9. If one apple is green and 7 are red, 0.125 of all the apples are green, not .125000000000001 or .12499999999999999.
If anyone has missed anything in math, it isn't me.
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1 apple is not exactly 1/8 of 8 apples.
Because there are no absolutely identical apples.
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Code for TallyGenerator -
I really like your choice in footwear.
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By the way, Giordy, don't you have some code to write to actually back you up?
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Of course it is 1/8 of 8 apples. We're discussing quantities, not weight or volume.
If I have 7 little Winesaps and 1 big honkin' Red Delicious, each one is still just 1 apple, and each one is 1/8 of 8 apples. In fact, if you take 1 away, you'll have 7 apples, no matter which one you take away. It's been a while, but I'm pretty sure that one was taught when I was 3. Skip that stage? Hell, even if 1 of the apples has a worm in it (we'll give that one to you), it's still 1 apple. It's also an apple with a worm in it, but that doesn't negate the fact that it's 1 apple.
If we really wanted to make fun of you, we could mention that if 1 apple isn't 1/8 of 8 apples because there are no "precise" numbers (your claim, not mine, but then it's not the first time you've been wrong in this thread), then there can't even be 8 apples, but that would make you look silly, and I don't think you need a hand with that.
There is this recent invention that we call "integers", which can be a hard concept to grasp, but people often find them quite useful when dealing with quantities. To help you out, I'll show you where you can find out about them, in case your employer decides they need a table that stores quantities for some strange reason. It's rare, but most of us who have thousands of tables have found a use for them in at least one column somewhere. Speaking of integers, this post is "precisely" 1 post in "precisely" 1 thread in "precisely" 1 forum on "precisely" 1 domain, even though this post increased the length of the thread, the number of posts in the forum, and the storage requirements of the domain (sorry Brian, Andy, and Steve).
I'd love to do your payroll. I'd pay you in "inprecise" dollars and cents, where each dollar is somewhere between 0 and 1 dollars. Sorry, but this week those dollars were a hell of a lot closer to zero (0.000000000001 dollars, to be "inprecise") than I was expecting. Better luck next time.
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David, just a quote from the article you referenced:
Now look at .99999999..... which is equal to 9/9 = 1.
So, if .99999999..... = 1 then 1 = .99999999.....
Right?
Well, now turn it over:
0.0000000....1 = 0
AND
0 = 0.0000000....1
Are you disagree with Dr. Math?
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Code for TallyGenerator -
Sergiy, You know how to end this. You either come up with a valid proof and support it or admit you were wrong. There is no shame in admiting ones mistake. The problem comes when you try to continuosly cover it up with misdirections and half truths.
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