[linux] Difference between using "chmod a+x" and "chmod 755"

Indeed there is.

chmod a+x is relative to the current state and just sets the x flag. So a 640 file becomes 751 (or 750?), a 644 file becomes 755.

chmod 755, however, sets the mask as written: rwxr-xr-x, no matter how it was before. It is equivalent to chmod u=rwx,go=rx.

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