Can Someone Explain the Set $\{ ∈ ℝ^ ∣ d(x,0) = 1\}$? I'm trying to understand this set. I understand most of the individual parts such as $∈$ means "an element of", $ℝ$ is all real numbers, and $d(x,0) = 1$ is the distance from $x$ to $0$, as in absolute value.
I don't understand what $x$ means in this situation though. Is it considered a variable? Is it multiple values? 
I also don't understand what the actual elements of the set are. Is the value of $x$ and element in the set? Also, are there any other numbers with an absolute value of $1$ other than $1$ and $-1$? If not, are those the only possible values for $x$? 
In this situation, $N$ is a number of dimensions, but I don't understand how that relates to real numbers, nor what real numbers to any power would be.
Thanks.

The notation $d(x,0)=1$ seems to indicate that this is a problem in a general metric space. This is not necessarily the absolute value, as there can be more abstract metrics. This set is the unit ball in $\mathbb{R}^N$ with respect to this metric. 
