By using this site, you agree to our Privacy Policy and our Terms of Use. Close
 

Which one?

Maths 19 26.76%
 
Math 20 28.17%
 
Mathematics 32 45.07%
 
Total:71
Aielyn on 02 April 2016
Teeqoz said:
Ljink96 said:
I have no words. This thing always gets me. Even with the idea of rounding it doesn't validate any other number's identity. Why just these two?! O.o

Actually, all truncated numbers have two notations.

1.5000... (or 1.5 as we'd normally write) is the same as 1.4999....

0.1000... is the same as 0.09999999 (this one is pretty easy to infer when one accepts that 0.999... is equal to 1, because 0.0999 is the same as 0.999.../10, and 0.1 is the same as 1/10, and because 0.999...=1, naturally 0.1 must be equal to 0.0999...)

Fixed it for you.



Around the Network
Teeqoz on 02 April 2016
JWeinCom said:
Teeqoz said:

It's not just a flaw with base 10 though. Base 3 also has fractions that can only be represented by infinitely recurring decimals. The only thing that changes when you change the base is what fractions.

If there is a system that has a flaw, then it's the decimal system itself. However I like to think of it as just another way of writing the same thing. 2/2 (As a fraction), 10^0, 1, 0.999.... All just different ways to write the value (not the number) 1. The recurring 9 notation works for all finite sequences of numbers as well (ie 0.25=0.24999....)

It's like a synonym in language. It's just that people are a bit more stuck up when it comes to math.

It may be a flaw in the system, but the flaw isn't that this should be incorrect, because it is correct. The flaw is that notation like this is ever used/ever has to be used. However when you denounce something as "simply the result of a flaw in the system", people are often quick to think "aha, so it's not actually correct", so you have to be careful when proclaiming things as the result of a flaw in the system.

I don't believe I said that the system is flawed.  I said it is limited which I'll stand by.  That's not to say other systems are not limited (I chose to use base 3 instead of base 2 because 1/3 and 2/3 still repeat there), but this particular example is one that exists in base 10 and not in other systems.

Still, when you say "it's only because of a limitation of the system", it has that same effect on people, ie. it makes them think "well, it is correct because of the limitations, but it's not really correct".

Also, to simply think of it as a limitation as to how our decimal system "displays" fractions isn't right, because the concept of 0.999... reccurring doesn't require you to think of it as 9 times 0.111.... reccurring, or 9*1/9. The fractions themselves are just used in (some) proofs. However you can prove that 0.999...=1 without using fractions, so they aren't the root of the problem. 

The phenomenon that one value can be written in two ways (ie. that 0.25 = 0.24999... etc. for any possible value) exist for all bases, the only thing that changes is which digit is repeated (it's the highest digit of any given base, so in base 9, the digit repeated would be 8, in base 8, the digit repeated would be 7. In base 3, fractions like 1/2 are infinite sequences of numbers (1/2 in base 3 being 0.111....)



sc94597 on 03 April 2016
fatslob-:O said:

As an aside how many people here know calculus or some elementary real anaylsis ?

I've taken a full Calculus sequence (and currently tutor it for extra cash while I study Physics), and learned Real Analysis from Apostol's Mathematical Analysis (I loved referencing his Calculus volumes when I was learning Calculus from Stewart's book - via my school's choice, so I decided to look at his intermediate text.) 



Aielyn on 03 April 2016
MohammadBadir said:
It's kinda hard to grasp. On one hand 0.33333 = 1/3 so 0.99999 should be 1, but on the other hand, it stars with 0 so it's technically an infinitesimal smaller :P

It's not. Decimal notation with the "..." at the end (or a bar over the repeating part) is actually shorthand for a mathematical limit. What 0.999999... actually represents is

sum from n=1 to infinity of 9/(10^n)

And that evaluates to 1. The fact that it "starts with zero" is irrelevant. Decimal notation is nothing more than a representation, it's not actually a number. 0.1111.... represents 1/9. 0.9999.... represents 1.



JWeinCom on 03 April 2016
Teeqoz said:
JWeinCom said:

I don't believe I said that the system is flawed.  I said it is limited which I'll stand by.  That's not to say other systems are not limited (I chose to use base 3 instead of base 2 because 1/3 and 2/3 still repeat there), but this particular example is one that exists in base 10 and not in other systems.

Still, when you say "it's only because of a limitation of the system", it has that same effect on people, ie. it makes them think "well, it is correct because of the limitations, but it's not really correct".

Also, to simply think of it as a limitation as to how our decimal system "displays" fractions isn't right, because the concept of 0.999... reccurring doesn't require you to think of it as 9 times 0.111.... reccurring, or 9*1/9. The fractions themselves are just used in (some) proofs. However you can prove that 0.999...=1 without using fractions, so they aren't the root of the problem. 

The phenomenon that one value can be written in two ways (ie. that 0.25 = 0.24999... etc. for any possible value) exist for all bases, the only thing that changes is which digit is repeated (it's the highest digit of any given base, so in base 9, the digit repeated would be 8, in base 8, the digit repeated would be 7. In base 3, fractions like 1/2 are infinite sequences of numbers (1/2 in base 3 being 0.111....)

People can think whatever they want about it.  The fact is that the system we use obviously has limitations.  Any system of symbolic representation does. 



Around the Network
Teeqoz on 03 April 2016
Aielyn said:
Teeqoz said:

Actually, all truncated numbers have two notations.

1.5000... (or 1.5 as we'd normally write) is the same as 1.4999....

0.1000... is the same as 0.09999999 (this one is pretty easy to infer when one accepts that 0.999... is equal to 1, because 0.0999 is the same as 0.999.../10, and 0.1 is the same as 1/10, and because 0.999...=1, naturally 0.1 must be equal to 0.0999...)

Fixed it for you.

I've never heard that word before. :/

While the language of math itself is international, some words which are related to math aren't, so I don't really know what that means :-3



fatslob-:O on 03 April 2016
sc94597 said:
fatslob-:O said:

As an aside how many people here know calculus or some elementary real anaylsis ?

I've taken a full Calculus sequence (and currently tutor it for extra cash while I study Physics), and learned Real Analysis from Apostol's Mathematical Analysis (I loved referencing his Calculus volumes when I was learning Calculus from Stewart's book - via my school's choice, so I decided to look at his intermediate text.) 

Neat, I too have done the entire calculus sequence except for the complex analysis but I've been meaning to get into abstract algebra specifically for group theory as I am interested in the applications along with the proofs ...



Teeqoz on 03 April 2016
JWeinCom said:
Teeqoz said:

Still, when you say "it's only because of a limitation of the system", it has that same effect on people, ie. it makes them think "well, it is correct because of the limitations, but it's not really correct".

Also, to simply think of it as a limitation as to how our decimal system "displays" fractions isn't right, because the concept of 0.999... reccurring doesn't require you to think of it as 9 times 0.111.... reccurring, or 9*1/9. The fractions themselves are just used in (some) proofs. However you can prove that 0.999...=1 without using fractions, so they aren't the root of the problem. 

The phenomenon that one value can be written in two ways (ie. that 0.25 = 0.24999... etc. for any possible value) exist for all bases, the only thing that changes is which digit is repeated (it's the highest digit of any given base, so in base 9, the digit repeated would be 8, in base 8, the digit repeated would be 7. In base 3, fractions like 1/2 are infinite sequences of numbers (1/2 in base 3 being 0.111....)

People can think whatever they want about it.  The fact is that the system we use obviously has limitations.  Any system of symbolic representation does. 

People can think whatever they want about it, but it doesn't make it true (or false). I'm not saying the system doesn't have limitations, I'm saying that just because the system has limitations does not mean that this is "sorta true, but not really true".



JWeinCom on 03 April 2016
Teeqoz said:
JWeinCom said:

People can think whatever they want about it.  The fact is that the system we use obviously has limitations.  Any system of symbolic representation does. 

People can think whatever they want about it, but it doesn't make it true (or false). I'm not saying the system doesn't have limitations, I'm saying that just because the system has limitations does not mean that this is "sorta true, but not really true".

And I didn't say anything like that... so I'm not sure what your point is here.



Aielyn on 03 April 2016
Teeqoz said:
Aielyn said:

Fixed it for you.

I've never heard that word before. :/

While the language of math itself is international, some words which are related to math aren't, so I don't really know what that means :-3

"Truncate" means stop after a certain point. A truncated decimal is one that stops after a certain point - in base 10, it's fractions whose denominators are a power of 2 multiplied by a power of 5.

1/3 has only one decimal representation - it's not a truncated decimal.