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Old 2007-04-23, 08:46   #12
davieddy
 
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Quote:
Originally Posted by mfgoode View Post
It is not a riddle! Its just a maths curiosity which looks odd and that it is wrong but it is right.

Mally
?????????

(ab)2=a2b2

Last fiddled with by davieddy on 2007-04-23 at 08:52
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Old 2007-04-23, 08:47   #13
drew
 
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Quote:
Originally Posted by mfgoode View Post
The version you have given is totally wrong
I'm continually amazed at how someone can be so consistently wrong about so many things.

You've outdone yourself, Mally.
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Old 2007-04-23, 08:53   #14
michaf
 
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More generally:

 a = \sqrt{a^2}
and
\sqrt{a}\cdot\sqrt{b} = \sqrt{ab}
thus  2 \cdot\sqrt{\frac{2}{3}} = \sqrt {2^2 \cdot \frac{2}{3})} = \sqrt{ 4 \cdot\frac{2}{3}}

(This is merely an excercise in TeX for me, been quite a while since last usage...and I sure hope nobody saw me struggling :>)

Last fiddled with by michaf on 2007-04-23 at 08:59
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Old 2007-04-23, 10:37   #15
davieddy
 
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Mally: is this something you tried on a calculator?
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Old 2007-04-23, 12:11   #16
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Of course, there is the calculator approach to it:

2*sqrt(2./3) = 1.6329931618554521
sqrt(4/3) = 1.1547005383792515
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Old 2007-04-23, 12:58   #17
R.D. Silverman
 
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Quote:
Originally Posted by michaf View Post
More generally:

 a = \sqrt{a^2}

False.


and
\sqrt{a}\cdot\sqrt{b} = \sqrt{ab}

False.
Your results (often stated) are false without carefully stating the
domain in which they apply. They are certainly NOT true over C
without stating which branch cut you are taking.
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Old 2007-04-23, 13:00   #18
davieddy
 
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Quote:
Originally Posted by fetofs View Post
Of course, there is the calculator approach to it:

2*sqrt(2./3) = 1.6329931618554521
sqrt(4/3) = 1.1547005383792515
But can Mally mangle the syntax sufficiently to
arrive at equality?

His resourcefulness in this respect is boundless:)

Last fiddled with by davieddy on 2007-04-23 at 13:05
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Old 2007-04-23, 13:30   #19
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Quote:
Originally Posted by drew View Post
I'm continually amazed at how someone can be so consistently wrong about so many things.
You've outdone yourself, Mally.
!

I think the first part (maybe not the second part) of R.D.Silverman's post gives an indication to the intended solution.

PS: well, there are several solutions... at least (a trivial) one is easy to see.

Last fiddled with by m_f_h on 2007-04-23 at 14:03
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Old 2007-04-23, 13:42   #20
davieddy
 
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Quote:
Originally Posted by m_f_h View Post


I think the first part (but not the second part) of R.D.Silverman's post gives an indication to the inteded solution.
Could you enlighten us as to this "solution" please.

David
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Old 2007-04-23, 13:50   #21
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Fields of finite characteristic? In characteristic 2, the two are indeed identical, as both are equal to 0. But if someone is asking such a question and has a domain other than the run-of-the-mill R or maybe C in mind, he must say so, or the question is ill-stated and quite meaningless.

Alex
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Old 2007-04-23, 14:04   #22
m_f_h
 
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Quote:
Originally Posted by akruppa View Post
Fields of finite characteristic? In characteristic 2, the two are indeed identical, as both are equal to 0.
This was the trivial one...
PS: and in an extension of R which has an absolute value, the equation is certainly wong, that's why it seems improbable that it's a question of branch cut.

Last fiddled with by m_f_h on 2007-04-23 at 14:09
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