$R/I$ when $R$ is the ring of real continuous functions If $R$ is the ring of all real continuous functions on $[0,1]$, I am trying to find $R/I$ where
$$I=\{f\in{R}|f(.5)=0\}$$
Showing $I$ is an ideal is not a problem since we're defining addition and multiplication as $$(f+g)(x)=f(x)+g(x).$$ 
$$(fg)(x)=f(x)g(x)$$but I'm trying to identify $R/I$.  I am new to ring theory and i'm having trouble with the math.  What do elements of $R/I$ look like?  I know that Ideals are analogues of normal subgroups in group theory and that normal subgroups are defined as 
$$N=\{a\in{G}|aH=Ha\}$$
where G is a group and H is a subgroup.
This makes sense to me with Ideals but I can't think of this in terms of continuous functions.  

What you have is that two elements $[f]$ and $[g]$ of the quotient are the same if and only if $f(0.5)=g(0.5)$. So, intuitively, what only matters for $[f]$ is only its value on $0.5$, therefore $R/I$ should be isomorphic to $\mathbb R$. Indeed, this is the case, and you can see that after considering the map Hagen von Eitzen mentioned above.
