# Difference between 2f+1, 2f and 3f+1

I am currently reading the Practical Byzantine Fault Tolerance paper. I am unable to completely understand the difference between 2f and 2f+1. If 2f+1 means that a majority of the nodes are non-faulty then what does 2f represent?

$2f$ and $2f + 1$ are just numbers. A set of $2f + 1$ nodes has a majority of non-faulty nodes, as you say; a set of $2f$ nodes can be deadlocked between the non-faulty and faulty nodes. A total of $3f + 1$ nodes are needed in the system to be able to construct a set of $2f + 1$ nodes when up to $f$ nodes are not responding (as outlined in section 3).