I always have this argument with my friends. Its about the rounding of numbers, i.e either the rounding up or down depending on rules set by mathematics.

However my argument is that, lets use the number 16, is to be rounded to the nearest tens, it would give you a rounding equal to 20. However if you bring in "general logic" and set aside the rules of mathematics it would make more sense to round down to 10, because you can always remove those 6 units that exist rounding down to 10, rather than adding an imaginary 4 units to 20, which do not exist. How can you add something that does not exist to something else, so it would make more logical sense to always round down?

My argument is not about how rounding solves problems in mathematics, accounting, etc, but that it would make more logical sense to round down than up. i dont want ppl sayin that rounding of course helps in money situations such as when the price is $9.99, my argument is that rounding down makes more sense than round up in the logical sense not in the mathematical sense.

Cheers

Those type question of questions never bother me, in math one does not approximate.

But I believe that this might help. Given a number and two approximanations , how can we tell which one is more accurate? We check wether,
---> more accurate
---> more accurate
---> equally accurte.

Where, means 'absolute value'.
Becase the absolute value measures the positive difference between two numbers. So we say one number is more accurate than another when its positive difference is less then the others positive difference. And this makes sense because the smaller the positive difference the closer it is to the actual value. Which is why the rules of rounding where taken the way they were.

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"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran

But rounding is only done as to put an answer in context, logically the actual answer will suffice.

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Vaiyo A-Rah
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Vaiyo A-Rah
Jerhume Brunnen G

Oh yes we do, all of the time.

Only in Hackerian Mathematics is approximation forbidden

RonL

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Truth does not change because it is, or is not, believed by a majority of the people.

Giordano Bruno

Logic has nothing to do with rounding, rounding is only done for
computational/mathematical purposes, so it is the needs of those
which determine how we round.

Your approach to rounding is without purpose and so irrelevant.

RonL

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Truth does not change because it is, or is not, believed by a majority of the people.

Giordano Bruno

When I was in high school chem I got into an argument about significant figures and medicine. She said it was extremely important in medicine and I told her that rounding in medicine could be dangerous. To address the OP, rounding is necessary and the rules are created to make the rounding as accurate as possible. As an aside, I think sig figs can be taken to an extreme. I hate to see people get upset over one extra decimal place. I think the main thing should be to note that if you measured some thing to be 1.01 meters (with accurary to the tenths place) , then a third of that is not
.33666666666666666667m.

Hackerian Mathematics is 100% Formal Mathematics.

Approximation is a good thing, and when I work on applied problems (yes I do sometimes ) for example the hanging cable problem I dropped the negative exponential so I solve it via the Lambert Function. But for a mathemation such an approach is forbidden.

It seems one day I will have a school of mathematical thought named after me.

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"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran

Or else you will be retired on the orders of the Head of the Numerical
Analysis family.

RonL

__________________
Truth does not change because it is, or is not, believed by a majority of the people.

Giordano Bruno

id like to thank everyone for their replies, but you's are not answering my question exactly. my question is "does it make more LOGICAL sense to round down than up according to my previous reason?"

i know that rounding helps in mathematics and computation, but lets jump out of this world for a second and step into things that logical sense rather than a world goverened by pre-approved laws and rules. And by logical i mean for example if a cars going to run you over, the most logical thing to do is move out of its path. So any answers referring to the set laws of mathematics and other stuff like that arnt what im lookin for.

so let me just present my case again. "Does it make more LOGICAL sense to round down than up becuase how can you add something that does not exist to something else?"

so if you's can set aside you calculators for a second and just think about this philosophically, im just lookin for yes or no answers with a reason why, that seems logical and without mathematical groundings!

thanks

If it's 1:19p.m. Would you like someone to say 1:15 or 1:20

If you have 4 dollars, would you say you have 0 dollars or five dollars.

Many times it doesn't make sense to round down.

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No. I already said, which ever one is closer to is the to makes more sense. But you are correct to say you can define the rule in any way. But what I do not understand is the purpose of this post?*)


*)Likewise you can say what is the purpose of pure math. It reminds me of a joke. A person was lost in a hot air ballon and scream, 'Can somebody help me'. In response he heard somebody scream 'No'. His partner said that must have been a mathemation because what is said was absolutely correct but utterly useless.

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"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran

Your example presupposes so much that it is a bad example of what most
people would regard as something making logical sense.

First it assumes that you can know that you will be run over,
then that existence is better than non-existence
then that your individual existence has higher utility to you than
your non-existence, and also that you have the power to move out
of its way.

Your unstated assumptions in your example are the equivalent of
my assumption that rounding has a purpose, and since this is a
process in arithmetic, arithmetical presuppositions are appropriate.

RonL

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Truth does not change because it is, or is not, believed by a majority of the people.

Giordano Bruno

Reminds me of a joke as well:

The head of Physics goes to see the Vice-Chancellor (that the Principal in
a UK University) to ask for a seven figure sum for the latest superconducting
super widget for their experiment at CERN.

The Vice-Chancellor tells him "Why can't you be more like the Maths
department all they ever ask for is money for pencils paper and waste paper
bins, or better yet the Philosophy department who only ever ask for money
for pencils and paper"

(This joke dates from before the era of large scale Computational Philosophy)

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Truth does not change because it is, or is not, believed by a majority of the people.

Giordano Bruno

ok, let me explain this to you's for the last time. lets imagine the notion of rounding figures did not exist, as in there was no reason for it to exist. Then one day someone comes to you and lies these rules of rounding figures in front of you.

Do you think that it would be a little illogical that rounding figures up, by ADDING IMAGINARY UNITS (my main concern) rather than rounding down and removing units that already exist. This is what im arguing about, adding imaginary units so the number jst seems illogical even to a mathematical point of view, how can u jst pull these numbers out from no where, even you guys can realise that point!!

So if you can forget ur mathematical knowledge behind, regardless of this is thinking logical or not, just what makes sense...

BTW captainblack, being that pedantic about the definition of logic or a possible example only further emphasises your inability to function as rest do in human society!

oh and theperfecthacka, cheers for the sensorship, i didnt kno that there were kid in this forum!!

eubaldo shout out!!

Please give an example of when it doesn't make sense to round up. I see what you're saying but can't think of any more examples...

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