There is a way to do this. Aptitude is only a layer abstraction on top of
dpkg that makes it more user-friendly, or easier to use, or safer, or less powerful, or patronizingly child-proofed depending on your relationship with your system and your outlook on life.
By definition, when you remove a package that is a (in this case a completely arbitrary) dependency, you are going to 'break the package' that depends on it. More often than you would think, this doesn't actually impair the functionality of the broken package perceptibly. Just always know that you can press
CTRL+ALT+F2 F3, F4, etc. once the OS is loaded and get a terminal to fix whatever you need to. Though you very well may have to be able to configure networking from the command line in that case... Anyways, If anyone tells you that "you can't", take it with a grain of salt. Because "you can".
Check that you got the right package name
~$ dpkg --list | grep "update-"
You should get some output like this with version numbers and some other info:
Cool. Now you can see that
update-notifier has another library associated with it
update-notifier-common. Let's remove these unnecessary packages. (Because seriously, let's face it, that ubuntu makes the entire gnome setup dependent on a GUI interface to an abstraction-layer of the Debian package manager is ridiculous.)
~# sudo dpkg -r --force-depends update-notifier
-r flag is short
--force-depends removes the package even though it breaks a dependency.
Or if you hate the thought of a bunch of configuration files for packages that you don't have on your computer laying around:
~# sudo dpkg -P --force-depends update-notifier
-P flag is Purge.
I usually restart at this point and check to make sure nothing I care about is broken. If it's all good, repeat the process for
update-notifier-common, and check again. You would be amazed at how much you can break and still have a fully functioning workstation.
And there you go. It's gone.
In fact, instead of
update-notifier you should just install
unattended-upgrades then run
dpkg-reconfigure -plow unattended-upgrades to automatically update unattended upgrades, and get the vital security updates without thinking about it ever again.
To reiterate: if this does break something you can't live without, you can always get to a terminal via
CTRL+ALT+F1 when the OS loads and reinstall the package. But seriously, if it's not a production system at work. Break it, and fix it, and break it again. Not only is it more fun, but you learn more faster. When you've messed around with packages enough to feel comfortable, I recommend moving on to kernel modules.
Seriously, I'm not joking. You will learn so much.