Disk problems and reinstalling Mavericks! This started after I installed a BootCamp Windows 8.1 partition. That partition ran out of space so I decided to not heed any warnings and tried to format my Macintosh HD into free space, 10G of free space. Still no problems until I decided to boot into Mac OS X and saw that I accidentally deleted my Mac OS X partition!

I booted into my Recovery partition and reinstalled Mavericks.

I formatted the Recovery HD partition as HFS.. since after I made free space it showed up in the Mac (This is before the reinstall)

So after the reinstall, I am here. I went into the terminal and merged the apple_boot recovery HD into the main Macintosh HD partition...
except, there was one more Recovery HD partition HFS?

So what I want to do is remake my partition map, like the manufacterer's default.

Is there a way I can reinstall Mac OS X Mavericks without external media? Is Internet Recovery built into the rMBP Late 2013 13"?

If so, can I use it, delete all of my partitions, and reinstall Mac OS X mavericks and will that installation also make a Recovery HD partition?

What do I do?

No backups needed.

updated

/dev/disk0
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *121.3 GB   disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:                  Apple_HFS MACINTOSH HD            89.4 GB    disk0s2
   3:                  Apple_HFS Recovery HD             650.0 MB   disk0s3
/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:                            Disk Image             *102.4 MB   disk1
/dev/disk2
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     Apple_partition_scheme                        *136.2 MB   disk2
   1:        Apple_partition_map                         30.7 KB    disk2s1
   2:         Apple_Driver_ATAPI                         2.0 KB     disk2s2
   3:                  Apple_HFS Recovery Disk Assistant 136.2 MB   disk2s3
/dev/disk3
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *1.0 MB     disk3
   1:                  Apple_HFS Minecraft               1.0 MB     disk3s1
/dev/disk4
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     Apple_partition_scheme                        *158.6 MB   disk4
   1:        Apple_partition_map                         32.3 KB    disk4s1
   2:                  Apple_HFS Google Chrome           158.6 MB   disk4s2

No CoreStorage logical volume groups found
So what I want to do is remake my partition map, like the
  manufacterer's default.


Based on your comments, you've managed to reclaim the space from the orphaned bootcamp partition and merge it into your boot volume. Assuming disk0s2 is now ~30 GB larger, the partition map listed for your internal boot drive /dev/disk0 is the default partition scheme.


  Is there a way I can reinstall Mac OS X Mavericks without external media? Is Internet Recovery built into the rMBP Late 2013 13"?


Yes. As you mention, using Internet Recovery. Hold down Option+Command+R at the boot chime to enter Internet Recovery. You'll be greeted with a spinning globe. Once loaded, from the main pane select "Reinstall OSX" and then select your internal drive as the destination. 


  If so, can I use it, delete all of my partitions, and reinstall Mac OS
  X mavericks and will that installation also make a Recovery HD
  partition?


Yes, if you wish, however you will lose all data on the internal drive during a clean wipe (reformat) and reinstallation. The reformat will wipe the drive. The reinstallation will reinstall OSX onto the boot volume, as well as recreating both the default EFI and Recovery partitions. To do so:


Enter Internet Recovery as mentioned above
Open "Disk Utility" from the main pane.  
select the whole boot Drive [IE 120 GB Apple SSD] > Erase tab > Format: Mac OS Extended (Journaled) > click "Erase..."
The drive is now reformatted and completely blank. 
Exit "Disk Utility" and Open "Reinstall OSX"
Select the Internal drive and let OS X install. Upon completion, the machine will reboot normally and you will be greeted with the Setup Assistant process.