Simple Arithmetic! - Page 2

davieddy · 2007-04-23, 08:46

Quote:

Originally Posted by mfgoode

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

drew · 2007-04-23, 08:47

Quote:

Originally Posted by mfgoode

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.

michaf · 2007-04-23, 08:53

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 :>)

davieddy · 2007-04-23, 10:37

Mally: is this something you tried on a calculator?

fetofs · 2007-04-23, 12:11

Of course, there is the calculator approach to it:

2*sqrt(2./3) = 1.6329931618554521
sqrt(4/3) = 1.1547005383792515

R.D. Silverman · 2007-04-23, 12:58

Quote:

Originally Posted by michaf

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.

davieddy · 2007-04-23, 13:00

Quote:

Originally Posted by fetofs

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:)

m_f_h · 2007-04-23, 13:30

Quote:

Originally Posted by drew

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.

davieddy · 2007-04-23, 13:42

Quote:

Originally Posted by m_f_h

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

akruppa · 2007-04-23, 13:50

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

m_f_h · 2007-04-23, 14:04

Quote:

Originally Posted by akruppa

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.

2007-04-23, 08:53	#14
michaf Jan 2005 479 Posts	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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2007-04-23, 10:37	#15
davieddy "Lucan" Dec 2006 England 1100101001010₂ Posts	Mally: is this something you tried on a calculator?

2007-04-23, 12:11	#16
fetofs Aug 2005 Brazil 2·181 Posts	Of course, there is the calculator approach to it: 2*sqrt(2./3) = 1.6329931618554521 sqrt(4/3) = 1.1547005383792515

2007-04-23, 13:50	#21
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	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