Why can you push multiple symbols on a PDA stack at once? I'm really new to learning about PDA's and stuff, i understand that on a edge between 2 nodes you'll have something like this a,b->c. This means:

if a is in the beginning of your string and b is on top of your stack you can 


remove a from your string (the one you run through the PDA), 
remove b from your stack
place c on your stack


and take the edge...

My book also tells me that you can place more then one symbols on your stack. For instance a,b->cd. 

I think this is because you can also have this edge  ε, ε -> c wich just puts c on the top of the stack, 

so a,b->cd between Node 1 and 2 can by replaced by Node1 - a,b->c - New node -  ε, ε->d -> Node2.
Can someone please confirm if this is correct?

the pda is defined as (Q,E,T,d,s,F) with


Q an finite collection of states
E a finite inputalfabet
T a finite stackalfabet
d a transitionfunction Q x E (including ε) x T (including ε) -> V collection of(Q x T (including ε))
s the startstate
F a collection of eindstates (subcollection of Q)
You always have to take out a symbol. So if we could only write a single symbol, we could never really build up stack content.

Writing more than two symbols is just syntactic sugar; we could easily simulate it with PDAs restricted to writing zero, one, or two symbols.