Auto wrap lines in vim without inserting newlines

How do set vim to wrap text without inserting newlines?

Basically:

• I want to have a max width, say 80 lines
• As I type out a paragraph, if a word passes the 80 line mark, it should wrap the entire word (no splitting the word)
• If I type more than a couple of lines, it should still be wrapping
• If I save the file, I shouldn't see any line breaks unless I explicitly hit Enter when typing in edit mode

I can get some of this behavior with:

:set textwidth=80
:set wrap

Except this will insert newlines, and I don't want it to insert newlines. I already tried this but it doesn't work.

Reducing the width of the window to circa 80 characters, set wrap, and set linebreak should satisfy all your requirements.

See :help 'wrap' and :help 'linebreak'.