A math puzzle for you!

anant_shah94 said:
if n=m
then 1 cannot equal 2 because then n and m are not the same
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The whole point is to figure out what is wrong with the string of equations as one leads into the other. It's a puzzle, you are meant to find the flaw and explain WHY 1=2 although the transition from one formulation of the equation to the other is mathematically correct.

Look at the equation and prove to me why it is wrong.
 
PMKeates said:
0.3r being equal to an integer is news to me!
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I know it sounds counterintuitive (blame schooling for that) but IT IS accurate and true. The mathematical community accepts it and it has been proven with various ways.

Check wikipedia for it (I think it's googling for 0.999 that brings up the link).

It is exactly the recurring figures equaling integers that allowed the concept of fractions to begin with. People have in their minds integers and decimals very well separated but in maths it's all different.
 
kgi said:
I know it sounds counterintuitive (blame schooling for that) but IT IS accurate and true. The mathematical community accepts it and it has been proven with various ways.

Check wikipedia for it (I think it's googling for 0.999 that brings up the link).

It is exactly the recurring figures equaling integers that allowed the concept of fractions to begin with. People have in their minds integers and decimals very well separated but in maths it's all different.
Click to expand...

eh?..I think you mean that recurring sequences are rational numbers. Easily proven, but i think you'll find you'd have a hard time proving that

0.777777777777777777... = x, where x is an integer :p

Anyway, no internet cookie for you for dividing by zero :(
 
anant_shah94 said:
no, 0.9 recurring is equal to an integer :p I think he just got his wording a bit wrong.

0.3r x 3 = 1

There is an infinitesimally small difference between the two numbers, so they are regarded as being the same.
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That's the crucial point here really, they're regarded as being the same, as the difference is negligible, however in the utmost detail they are different.
 
DAnDan said:
That's the crucial point here really, they're regarded as being the same, as the difference is negligible, however in the utmost detail they are different.
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In the utmost detail? I'd say that they are regarded as the same even in the utmost detail.
This is proven by



1/3 x 3 = 1
1/3 = 0.3r

therefore 0.3r x 3 = 1

Mathematically they are no different
 
gambitt said:
Please explain.
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0.99r is 0.99999 taken to infinite length, it will always be 0.xxx1 (obviously the same amount as the amount of reoccurring 9s) away from 1. It's just as the difference is so negligible at that level of detail, you can discount it for most equations.
 
anant_shah94 said:
In the utmost detail? I'd say that they are regarded as the same even in the utmost detail.
This is proven by



1/3 x 3 = 1
1/3 = 0.3r

therefore 0.3r x 3 = 1

Mathematically they are no different
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I'd diagree, however I only have maths to A level, so may well be totally wrong.

The way I see it;

1/3 = 0.3r

0.3r = 0.9r (Still a minute bit less than 1).
 
DAnDan said:
0.99r is 0.99999 taken to infinite length, it will always be 0.xxx1 (obviously the same amount as the amount of reoccurring 9s) away from 1. It's just as the difference is so negligible at that level of detail, you can discount it for most equations.
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Where did the 1 come from?
 
DAnDan said:
0.99r is 0.99999 taken to infinite length, it will always be 0.xxx1 (obviously the same amount as the amount of reoccurring 9s) away from 1. It's just as the difference is so negligible at that level of detail, you can discount it for most equations.
Click to expand...

That would be true if 'infinity' acted like a number, but it doesnt.
Maths can get a little bit sticky when you reach infinite values, and one must take great care.

say we take a recurring sequence of 9s of length n, where n is an integer.

so, we have 0.9...9. and that's 0.0...1 away from 1, as you rightly said.

But any sort of 'infinity' isnt an integer. It isnt a rational, it isnt even real. So you can't apply the same principles we would normally apply to a finite value to an infinite value.
 
I always explain it like this.

1 - 0.99r = 0.000..000..00 forever and ever and ever and ever...000...never ending zeros..000...00000000....

So where does the 1 go? You can't just plonk it on the "end".
 
This 0.9999999999999999 r nonsense is a lot of bull !

Imagine 0.99999999999999999r light years in distance....

Even if you take it to a million places its STILL not a full light year and would be short by some distance. Even if you take it to 10 million, it would still be short again, which is not a full light year...

Ok you might be a few mm short, but its still short.
 
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