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math

ahsam imtiaz
prove that a real number can never equal to imaginary number
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Re: math

Robert Hansen
No real number satisfies the equation x^2 = -1.
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Re: math

Bishop, Wayne-2
In reply to this post by ahsam imtiaz

Try starting with precise definitions.  


Wayne

From: [hidden email] <[hidden email]> on behalf of ahsam imtiaz <[hidden email]>
Sent: Saturday, December 9, 2017 1:59 AM
To: [hidden email]
Subject: math
 
prove that a real number can never equal to imaginary number
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Re: math

Joe Niederberger
In reply to this post by ahsam imtiaz
asham says:
>prove that a real number can never equal to imaginary number

Wayne Bishop says:
>Try starting with precise definitions.

By any number of approaches (see Wikipedia, for example) I think we would see that zero is both real and imaginary, and that makes the statement false. If one disagrees with that, its because they like definitions that are crafted to avoid that conclusion, much like politics.

Cheers,
Joe N
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Re: math

Robert Hansen
In reply to this post by ahsam imtiaz
Joe wrote...

"By any number of approaches (see Wikipedia, for example) I think we would see that zero is both real and imaginary, and that makes the statement false. If one disagrees with that, its because they like definitions that are crafted to avoid that conclusion, much like politics."

I didn't search long, but the arguments for zero being both real and imaginary seem to involve complex numbers and the complex plane. For example, since the two axes of the complex plane intersect at 0 then 0 must be both real and imaginary. But the axes don't intersect at 0, they intersect at (0,0). Likewise, the notion that 0i is 0 (in the context of this problem) is also troublesome. When you reduce 0i to 0, it is no longer imaginary or complex. Do you know of any approaches that avoid this dilemma? I guess it comes down to the definition of imaginary itself, which is a number involving i. 0i is imaginary, but 0 (without the i) is not.

Bob
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Re: math

Bishop, Wayne-2

>   it comes down to the definition of imaginary itself, which is a number involving i. 0i is imaginary,


It is only a matter of definition because that is not my definition of imaginary.   An element of the field of complex numbers?  Absolutely.  An element of the subgroup of imaginary numbers I = {bi|b in R}?  Again absolutely. But my definition of imaginary number is a complex number a + bi with a = 0 and b nonzero.

Wayne

From: [hidden email] <[hidden email]> on behalf of Robert Hansen <[hidden email]>
Sent: Friday, December 15, 2017 3:37 AM
To: [hidden email]
Subject: Re: math
 
Joe wrote...

"By any number of approaches (see Wikipedia, for example) I think we would see that zero is both real and imaginary, and that makes the statement false. If one disagrees with that, its because they like definitions that are crafted to avoid that conclusion, much like politics."

I didn't search long, but the arguments for zero being both real and imaginary seem to involve complex numbers and the complex plane. For example, since the two axes of the complex plane intersect at 0 then 0 must be both real and imaginary. But the axes don't intersect at 0, they intersect at (0,0). Likewise, the notion that 0i is 0 (in the context of this problem) is also troublesome. When you reduce 0i to 0, it is no longer imaginary or complex. Do you know of any approaches that avoid this dilemma? I guess it comes down to the definition of imaginary itself, which is a number involving i. 0i is imaginary, but 0 (without the i) is not.

Bob
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Re: math

Joe Niederberger
In reply to this post by ahsam imtiaz
I not going to explain in depth, but to my ears this is sounding a bit like my puzzle about an infinity of 1s followed by an infinity of 0s, etc. Slight but annoying ambiguity about just what these supposedly abstract, yet still slightly typographical objects are.

Cheers,
Joe N