iCloud synchronized Notes still seem to keep a local copy of the note on the device, iPad or iPhone

Thank you for your response.

However, with your answer, I do not understand why Apple put this in their official iCloud user guide as quoted below:

"Keep your notes up to date and share them with iCloud

With iCloud, your notes stay up to date on all your devices and you can collaborate on notes with friends and family.

Access the same notes on all your devices

When you set up iCloud for Notes,

your notes are stored in the cloud, which frees up space on your

device. You can see them on any device that’s set up for iCloud and

Notes, including your iPhone, iPad, and Mac. You can also access your

iCloud notes in a web browser at iCloud.com.

Because your notes

are in the cloud, changes you make on one device—like creating a new

note, deleting a note, or editing the text—automatically appear on all

your devices. You see the most up-to-date version of your notes, no

matter where you access them."

The problem is with the part I italicized above: "When you set up iCloud for Notes,

your notes are stored in the cloud, which frees up space on your

device."

This leads me to believe that when you synch Notes to iCloud and write a new note in iCloud, the note is not saved on the local device, but only in iCloud. Why does the manual say that such an operation frees up the space on your device contrary to what you said in your commentary?