# Quick Denotation Question

• Sep 26th 2011, 06:53 PM
Sw0rDz
Quick Denotation Question
$\displaystyle R^\times$ and $\displaystyle C^\times$ mean when referred to the following example:

Does there exist an isomorphism from $\displaystyle C^\times$ to $\displaystyle R^\times$.

I have a fairly good idea on how to solving this, but I can't really solve it w/o the ability to read the denotation.

Thanks!
• Sep 26th 2011, 06:59 PM
dwsmith
Re: Quick Denotation Question
Quote:

Originally Posted by Sw0rDz
$\displaystyle R^\times$ and $\displaystyle C^\times$ mean when referred to the following example:

Does there exist an isomorphism from $\displaystyle C^\times$ to $\displaystyle R^\times$.

I have a fairly good idea on how to solving this, but I can't really solve it w/o the ability to read the denotation.

Thanks!

dual space maybe
• Sep 27th 2011, 03:03 AM
emakarov
Re: Quick Denotation Question
Maybe its an isomorphism between the multiplicative groups of $\displaystyle \mathbb{C}$ and $\displaystyle \mathbb{R}$.
• Sep 27th 2011, 03:34 PM
Drexel28
Re: Quick Denotation Question
Quote:

Originally Posted by Sw0rDz
$\displaystyle R^\times$ and $\displaystyle C^\times$ mean when referred to the following example:

Does there exist an isomorphism from $\displaystyle C^\times$ to $\displaystyle R^\times$.

I have a fairly good idea on how to solving this, but I can't really solve it w/o the ability to read the denotation.

Thanks!

I would tend to agree with emakarov that $\displaystyle \mathbb{R}^\times$ denotes the group of units of $\displaystyle \mathbb{R}$ and similarly for $\displaystyle \mathbb{C}^\times$. So, what is your proof? There is an easy way and a hard way.