Why won't my Nikon D3300 take more than 1000 photos?

I've only had this camera a few months and I can't figure out why I can't take over 1000 photos. I rang Nikon today and they were pretty useless but they told me I should be able to take up to 9999 photos. Problem is, if I take 1001, 1002, 1003 etc photos then it starts to rewrite over photo 001, 002, 003 etc (and for some reason it doubles the file too, so when I look at them on the computer there are two copies of each shot). I technically can keep shooting but I will lose the first 1000 photos I started with. Why is this happening? My memory card is big enough to take over 2000 photos. The guy from Nikon told me to turn ON the setting File Number Sequence but I'm not in the mood right now to take 1000 photos to test out if this has fixed the problem.

WOW

Nikon gave you good advice. Use the menu to set your file numbering system to sequential. That is what about 99.99999% of the world does.

Secondly, at the end of each shooting day, copy all the images to your computer to a new file folder named for the subject/location and date by inserting your memory card into a card reader, either the one on your computer or a USB card reader that you bought.

Once all the image files are safely on your computer, insert the memory card into your camera and format the memory card so it is ready for your next adventure. You need to do this routinely so that you do NOT end up with a corrupted memory card and possibly losing all the images that are on the card

NOTE: Using a fully adjustable camera like the D300 is NOT about your mood. It is about using the cameras controls and different lenses to produce amazing images. The control has to be logical. The way you create the final image can and usually does reflect your feelings or mood

It's not the camera, it's the file numbering system. If your camera gets to 1,000 photos, it will create a new folder. When I shoot an event, I'll take over 1,000 photos, easily.

The Nikon guy gave you sound advice, because it's always worked for me.

When you store your photos on your computer, you can easily renumber any duplicates. Change some of the duplicates from DSC files to ones that use your initials, or any other 3 letter prefix you choose.

Here's some other techniques for you to explore.
http://darrellyoung.blogspot.com/2011/08/using-nikons-file-naming-and-file.html

One other thing, be sure you have the latest firmware. Nikon has had problems in the past with file folders being created prematurely in the past and was fixed with installing the latest firmware.

So Nikon has offered the solution but you're too lazy to verify if it worked and yet they're the one useless? Pass.

Why do you want to keep 1000 photos on your camera?
Just download them to your computer on a regular basis and re-set the numbering.