Relation among cluster member, blade, nodule, slot and partition

you seem to be asking a lot of basic f5 questions, which of course is good but makes me wonder if it wouldn't be smarter to have a chat with your f5 sales team or an f5 partner. you will get some answers here but for the big picture it might be useful to have a proper chat and not a few some questions that pop up.

cluster(member) - a big-ip in a DSC (device service cluster)

blade - within a viprion chasis you have one or more blade, see those a multiple big-ip working together

module - probably one of the software modules you can use: LTM, ASM, ...

slot - installation target for the tmos software, you can have several of these

partition - you can have multiple management sections in a big-ip, see the drop down in the right top corner.

if you search ask.f5.com you will find much more information about these.