Acknowledgments are arithmetic over sequence numbers. This lesson uses the same timeline twice to show that each SYN is acknowledged as one past the sender's sequence number.
highlighted = computed this step
Why acknowledgments point forward
An acknowledgment names the next sequence number expected from the other side. For the SYN segments in this book, that means one past the peer sequence number.
advance=1
Server acknowledges the client
The client SYN used 1000, so the server's acknowledgment is 1001.
1000+1=1001
Client acknowledges the server
The server SYN used 3000, so the client answers with acknowledgment 3001.
3000+1=3001
Decode it again
With client starting number 5000 and server starting number 9000, the acknowledgments become 5001 and 9001.
5000+1=5001,9000+1=9001
Summary
The ACK rule is local and exact: acknowledge one past the SYN sequence number being answered. Connection setup ordering and exact sequence numbers only; timing, retransmission, and round-trip time are not modeled here.