Are decimals flawed

[cheesy999]

*swoosh* now the talk goes above my head

other numbers used by other people

Roman Numerals - you may recognise as I II III IV V VI VII VIII IX X XI XII from a clock

Attic numerals were the number system used by the ancient greeks

Under ours

1+1=2 10+5 = 15

under Roman

I+I=II X+V=XV

 

[Bo$$]

But this all depends on what aspect you are working problems out, engineers a different methodology for compensating for decimals than, pure mathematicians or physicists require as their work and whole thought process is different.

 

[Fourstaff]

But this all depends on what aspect you are working problems out, engineers a different methodology for compensating for decimals than, pure mathematicians or physicists require as their work and whole thought process is different.

This sums up nicely Notice how mathematics is further away from sociology than physics is.

 

[Bo$$]

http://imgs.xkcd.com/comics/purity.png

This sums up nicely Notice how mathematics is further away from sociology than physics is.

i was looking for that one

where do the engineers come, in between the meths and physics
edit: maths*

 

[erocker]

Numbers along with decimals are not flawed. As a matter of fact they are perfect and can go in infinite directions.

 

[newtekie1]

Decimals aren't flawed, rounding is...

 

[HTC]

Decimals aren't flawed, rounding is...

Yup!

Reminds me of that classic story about the turtle and the rabbit: turtle was 100m in front of the rabbit and the rabbit was chasing the turtle. For ever 10m the rabbit ran, the turtle "ran" 1m.

Did the rabbit ever caught the turtle or not?

 

[Kreij]

rounding isn't flawed, ask any good carpenter. If it fits without a gap, it's right.

 

[FordGT90Concept]

if so, is there a number system under which these problems do not occur?

Fractional notation. Instead of turning 1/3 into 0.3333333, leave it 1/3. I even use fractional in some of my programs when 1/3+2/3 can't equal 0.99999999. This is also how the best graphing calculators work (e.g. TI-89 and TI-92).

why use decimals if their not good?

In the context of computers, because they are designed to handle decimals and not fractions. Fractions take up more memory and require more steps to perform mathematical operations on. With decimals, they can fly through the 128-bit FPU in the CPU in just a few CPU cycles. Moreover, often the precision of fractions isn't required in a lot of computing tasks (like graphics).

 

[theJesus]

why use decimals if their not good?

Because 4/3 of the population has trouble with fractions.

 

[mlee49]

Decimals aren't flawed, rounding is...

You'd be surprised how much is basically rounded. Some digital signal processing is not truly 1 or exactly 0 but because it's 0.99999 it's practically 1.

 

[twilyth]

It's too bad no one here realizes that this is an attempt at illustrating Godel's incompleteness theorems

http://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems

 

[Meaker]

my sig has all the answers you need

You do like dividing by zero don't you.

 

[1freedude]

number systems

Binary and hex...no decimals for obvious reasons. Clock systems usually have finite divisions, without a . and numbers behind it.

I deal with addition of decimals to the third place at work. We are adding areas in square inches. Very simple stuff, until it hits a maximum...local or absolute. To put it bluntly, the people that add these numbers don't give a shit about fractional repetition or rounding. If either of these maximums are exceeded, we (the company) have to spent a ridiculous amount of money to correct it.

 

[MilkyWay]

Our numerals are called Arabic numerals.
0.333^ Its basically infinite isn't it?

Apparently they try to explain this by saying its not 1 but 0.999^, its almost one! Think of it this way if you look at 0.999^=1 then your saying 1 doesn't exist nothing is quite complete and 1 is just a stand in for 0.999^ because we have to round up numbers because you cannot calculate an infinite number because it never ends.

(0.99^x10)-0.99^=9

1/3= .333...
2/3= .666...
3/3= .999...

but 3/3 =1?

HOLY FUCK! MY MINDS BLOWN!

 

[FordGT90Concept]

1/3 is infinite .3333
2/3 is infinite .6666
3/3 is 1 (3 can go into 3 once).

The problem with decimial is preserving the infnite (fractional has no infinite to preserve). The same issue arises in pi and imaginary. If you somehow preserve the infinite, 1/3 + 2/3 is 1; however, if the infinite is lost and it isn't rounded (.67 instead of .66), you get an infinite .9999. 1/3 + 2/3 is always 1 unless you convert to decimial and lose the infinite.

 

[twilyth]

I've seen this example before and whether it points out a flaw in our number system or not, I don't think it matters. Just read the first paragraph of the the link I posted previously. Godel's incompleteness theorems say that no purely axiomatic, deductive system can derive all true conclusions consistent with the axioms.

In the case of natural numbers, this means that no numeric system can deductively prove all true statements about natural numbers. If you find a system that does, then virtually by definition, the system is flawed.

I don't know how much sense that explanation made, but once you get it, your mind will be blown. Basically Godel proved that no purely deductive system based on a certain set of axioms can ever describe it's subject matter completely. If it does, then it is self contradictory in some respect. And remember, this isn't just another theory, he proved this to an absolute certainty.

 

[Fourstaff]

I've seen this example before and whether it points out a flaw in our number system or not, I don't think it matters. Just read the first paragraph of the the link I posted previously. Godel's incompleteness theorems say that no purely axiomatic, deductive system can derive all true conclusions consistent with the axioms.

In the case of natural numbers, this means that no numeric system can deductively prove all true statements about natural numbers. If you find a system that does, then virtually by definition, the system is flawed.

I don't know how much sense that explanation made, but once you get it, your mind will be blown. Basically Godel proved that no purely deductive system based on a certain set of axioms can ever describe it's subject matter completely. If it does, then it is self contradictory in some respect. And remember, this isn't just another theory, he proved this to an absolute certainty.

There are indeed proofs that says our number theory will never be made complete. We can use fancy axioms involving infinity and stuff like that to have a complete number theory, but we know that the axioms are shaky at best, false at worst. Welcome to the harsh world, where our understanding of the universe is based on an incomplete system.

 

[cheesy999]

I've seen this example before and whether it points out a flaw in our number system or not, I don't think it matters. Just read the first paragraph of the the link I posted previously. Godel's incompleteness theorems say that no purely axiomatic, deductive system can derive all true conclusions consistent with the axioms.

In the case of natural numbers, this means that no numeric system can deductively prove all true statements about natural numbers. If you find a system that does, then virtually by definition, the system is flawed.

I don't know how much sense that explanation made, but once you get it, your mind will be blown. Basically Godel proved that no purely deductive system based on a certain set of axioms can ever describe it's subject matter completely. If it does, then it is self contradictory in some respect. And remember, this isn't just another theory, he proved this to an absolute certainty.

There are indeed proofs that says our number theory will never be made complete. We can use fancy axioms involving infinity and stuff like that to have a complete number theory, but we know that the axioms are shaky at best, false at worst. Welcome to the harsh world, where our understanding of the universe is based on an incomplete system.

so you guys are saying these contradictions are unavoidable and will always happen no matter how someone changes the number systems?

 

[Fourstaff]

so you guys are saying these contradictions are unavoidable and will always happen no matter how someone changes the number systems?

In a nutshell, yes.

 

[cheesy999]

In a nutshell, yes.

i'd thank you but the button to do so isn't there any more

 

[slyfox2151]

i'd thank you but the button to do so isn't there any more

i thanked him for you

 

[qubit]

Decimals are not flawed.

Decimals and vulgar fractions simply have different properties. For example, you can't express an irrational number such as PI or e using vulgar fractions, but you can with decimals.

Similarly, decimals that repeat endlessly often can be expressed exactly using vulgar fractions.

There's other significant differences in properties, but I don't know what they are off the top of my head.

Search decimals and vulgar fractions on Wikipedia for more details.

 

[cheesy999]

you can't express an irrational number such as PI or e using vulgar fractions, but you can with decimals.

can't you just express them in terms of pie?

 

[qubit]

can't you just express them in terms of pie?

eh? That makes no sense.