Square root of a negative number? Say whaaat?

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Reply Fri 14 Nov, 2008 08:39 pm
Square root of a negative number? :shocked:

Does anyone here believe in this chimera? :sarcastic:

On another forum someone in all seriousness suggested that such things were possible.

Now I can say the number X is bigger than 10 whilst also being less than 5, and it is a single number, not a set of numbers.

And I could claim that such a number is imaginary.

But I would be speaking out my posterior. :bigsmile:

:whistling:
 
Aedes
 
Reply Fri 14 Nov, 2008 09:40 pm
@Poseidon,
There can't be a square root of a negative number. Unless today is opposite day.
 
paulhanke
 
Reply Fri 14 Nov, 2008 09:50 pm
@Poseidon,
Poseidon wrote:
And I could claim that such a number is imaginary.


... in which case you'd be exactly right Smile ... Imaginary number - Wikipedia, the free encyclopedia ... this is an example of how a nonsensical mathematical concept (square root of a negative number) can be employed in various symbol manipulations (equations) to produce a result that is meaningfully isomorphic with some aspect of the real world ... in mathematics, nonsense can beget sense Wink
 
Poseidon
 
Reply Fri 14 Nov, 2008 10:37 pm
@Poseidon,
Thanks guys.

I was really getting worried there for a minute.
 
manored
 
Reply Sun 16 Nov, 2008 02:58 pm
@Poseidon,
If someone shows you a rock claiming it to be a monkey, consider the possibility of the person being insane or intending you to imagine it as a monkey before considering the possibility of the rock being in fact a monkey.
 
validity
 
Reply Sun 16 Nov, 2008 09:38 pm
@Poseidon,
Poseidon wrote:
Square root of a negative number? :shocked:

Does anyone here believe in this chimera? :sarcastic:

On another forum someone in all seriousness suggested that such things were possible.

Now I can say the number X is bigger than 10 whilst also being less than 5, and it is a single number, not a set of numbers.

And I could claim that such a number is imaginary.

But I would be speaking out my posterior. :bigsmile:

:whistling:


The claim that such a number is imaginary is not what is meant by imaginary numbers. Numbers come in many different contexts and in the above post you have taken natural numbers out of context ie 10 can never be less than 5, by definition.

paulhanke wrote:
... in which case you'd be exactly right Smile ... Imaginary number - Wikipedia, the free encyclopedia ... this is an example of how a nonsensical mathematical concept (square root of a negative number) can be employed in various symbol manipulations (equations) to produce a result that is meaningfully isomorphic with some aspect of the real world ... in mathematics, nonsense can beget sense Wink


It is not nonsensical when taken in the correct context ie that of Complex Numbers Complex number - Wikipedia, the free encyclopedia
 
paulhanke
 
Reply Sun 16 Nov, 2008 10:19 pm
@validity,
validity wrote:
It is not nonsensical when taken in the correct context ie that of Complex Numbers Complex number - Wikipedia, the free encyclopedia


... unless I'm mistaken, it's just nonsensical, period ... "square" takes a geometric interpretation of a number as the length of one side and computes the area of the square ... "square root" is the complementary geometric interpretation of a number as the area of a square and computes the length of one of its sides ... since squares do not have negative areas, the notion of a square root of a negative number is nonsensical in and of itself ...
 
validity
 
Reply Sun 16 Nov, 2008 11:12 pm
@paulhanke,
paulhanke wrote:
... unless I'm mistaken, it's just nonsensical, period ... "square" takes a geometric interpretation of a number as the length of one side and computes the area of the square ... "square root" is the complementary geometric interpretation of a number as the area of a square and computes the length of one of its sides ... since squares do not have negative areas, the notion of a square root of a negative number is nonsensical in and of itself ...


Are we discussing the nonsensical nature of imaginary numbers or the nonphysicality of negative numbers? Within the framework of Complex Numbers, the sqrt-1 is perfectly sensible, because this framework defines imaginary numbers, thus allowing them to have meaning and use. Of course squares made of natural numbers do not have negative areas but in the framework of complex numbers sqrt-16 can be simplifed as

sqrt-1 x sqrt16

and by the definition sqrt-1 = i = imaginary number

sqrt-16 = 4i
 
paulhanke
 
Reply Mon 17 Nov, 2008 09:24 am
@validity,
... I think we're talking about the nonsensical nature of imaginary/complex numbers from the geometry and number theory perspectives ... as I mentioned before, the nonsensical nature of imaginary/complex numbers does not preclude their use in various symbol manipulations, the products of which can be mapped to the real world - but that tends to require imaginative (pun intended!) interpretation in which "i" is discarded from the result (e.g., interpreting the magnitude of the real part of a complex number as amplitude and the magnitude of the imaginary part as phase) ...
 
Owen phil
 
Reply Mon 21 Dec, 2009 06:34 am
@Poseidon,
Poseidon;33389 wrote:
Square root of a negative number?

Does anyone here believe in this chimera?

On another forum someone in all seriousness suggested that such things were possible.

Now I can say the number X is bigger than 10 whilst also being less than 5, and it is a single number, not a set of numbers.

And I could claim that such a number is imaginary.

But I would be speaking out my posterior.



Complex numbers (a+bi) are indeed just as real as are 'real' numbers.

Real and Imaginary are classifications of number, not literal descriptions of them.

There is nothing imaginary about the root of negative numbers.

There is an endless number of numbers such that their square is -1, and they are not equal to each other.

For example: 4-d hypercomplex numbers a+bi+cj+dk, where a,b,c,d, are real and [ i^2=j^2=-1, ij=ji=k, ik=ki=-j, jk=kj=-i, k^2=+1, ~(i=j), ~(i=k), ~(j=k).]
 
Reconstructo
 
Reply Mon 21 Dec, 2009 06:45 am
@Poseidon,
yeah "i" is the square root of -1
 
manored
 
Reply Mon 21 Dec, 2009 12:46 pm
@Poseidon,
Imaginary numbers are tricky, but they get easier to understand if you stop thinking of then as numbers and start thinking of then as positions in a graph. At least I think thats how the hell they are used in eletronics =)
 
Reconstructo
 
Reply Mon 21 Dec, 2009 04:39 pm
@Poseidon,
Math is wicked. Imaginary numbers and irrational numbers. It's poetry. I've been reading about Cantor and infinite sets. Great stuff.
 
Deckard
 
Reply Mon 21 Dec, 2009 06:04 pm
@Poseidon,
All numbers are imaginary (in one sense of the word).
(but yes I know about i)
 
Reconstructo
 
Reply Mon 21 Dec, 2009 08:08 pm
@Deckard,
Deckard;113354 wrote:
All numbers are imaginary (in one sense of the word).

Very good point. Very good point.
 
Owen phil
 
Reply Tue 22 Dec, 2009 01:15 am
@Deckard,
Deckard;113354 wrote:
All numbers are imaginary (in one sense of the word).
(but yes I know about i)


Bertrand Russell referred to nmbers as "convenient fictions".
 
Reconstructo
 
Reply Tue 22 Dec, 2009 01:23 am
@Poseidon,
You can only have a slice of pi, never the whole pi.
 
amer
 
Reply Wed 23 Dec, 2009 06:57 pm
@Poseidon,
Not only is this possible it is actually true. These are called imaginary numbers and denoted with the letter i. These numbers are extensively used in mathematics and physics.

---------- Post added 12-23-2009 at 08:02 PM ----------

I wouldn't trust Russel's judgement too much. This is a man who spent years and 200 pages proving via formal logic that 1+1=2 and then realized after reading Godels Incompleteness Theorem that the logic he used was fundamentally flawed.
 
Zetherin
 
Reply Wed 23 Dec, 2009 07:03 pm
@Deckard,
Deckard;113354 wrote:
All numbers are imaginary (in one sense of the word).
(but yes I know about i)


Which sense of the word would that be?

Owen wrote:
Bertrand Russell referred to nmbers as "convenient fictions".


What sort of thing, if any, do you think Russell would call a "convenient non-fiction", or just a "non-fiction"?

And, what do you make of this "convenient fiction"? What does it mean to you?

amer wrote:
Not only is this possible it is actually true. These are called imaginary numbers and denoted with the letter i. These numbers are extensively used in mathematics and physics.


What is actually true? Were you answering the OP, or concurring with something stated just above you?
 
amer
 
Reply Thu 24 Dec, 2009 02:53 pm
@Zetherin,
I thought I read a post that questioned the existence of imaginary (complex numbers) and I was responding to that.
 
 

 
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