Subject: How can we see a galaxy 13 billion light years away

Ok, with a very big telescope I suppose is a good answer but.... 

2 assumptions 
1) As we look at a galaxy we are looking back into time and across a distance. 
2) The universe started out as a singularity 

Now we can apparently look at a galaxy 13.4 billion light years away. This is 
how far it is away but also how old we are looking back - i.e. 13.4 billion 
years into the past. 
The universe is about 14 billion years old 
Since the light as taken 13.4 billion years to reach us it was 13.4 billion 
light years away 13.4 billion years ago 

13.4 billion years ago is about 600 million years after the big bang 
therefore the galaxy must have moved 13.4 billion light years in 600 million 
years - which is impossible. I know space is expanding but surely its not or has 
not expanded faster than the speed of light ?

I realise there must be a mistake in my understanding but I can't see it. Any 
ideas anyone

Re: How can we see a galaxy 13 billion light years away