The new owner will not need to purchase a SDJ license anymore than you did when you purchased it. Just keep in mind though the second you get rid of the SX you no longer have a license either.

yip unless you already purchased a full version of Serato DJ :)

I ONLY HAVE THE SERATO CD INSTALLER DO I NEED A SERIAL NUMBER OR SOMETHING I CAN,T REMEMBER WHAT I USED? IS THE SERATO CD INSTALLER SUFFICIENT FOR THE NEW OWNER AND WILL HE RECEIVE ALL THE EFFECTS I'VE PURCHASED IN THE PAST OR NO?

Any expansion packs you purchased will remain with your Serato account. The CD installer is not necessary at all as the SDJ version included on it is no doubt outdated anyways. The new buyer of your SX simply needs to download in stall latest version of SDJ from Serato.com and possibly the most current drivers and firmware from Pioneer.com.

btw any reason you are typing in all caps?

www.pioneerdj.com rather.

serato is registered to the controller you don't get any serial number if its bundled with a controller, you would have to buy a serato license if you want to keep using it after selling you sx

You really don't need to use all caps.

You do not own SDJ. Your controller does.
You sell the controller, you sell SDJ.

The install CD is irrelevant. The 'licence' is part of the controller.
If you want SDJ, you need to either buy a licence, or hardware that supports 'full' SDJ.