You can remove Cortana from the taskbar easily enough. Removing her completely, I dunno.

Just right click her and hide her, if you don't want the bitch down there....

Take a look at majorgeeks under System Tools>Windows 10 Fixes, you should find something there to do what you want.

I don't trust or use Cortana, either, and rely on my own wits to remember appointments, etc.  In fact, I use Win 10 like a regular OS, without the apps and other crap it comes with.  All that got uninstalled or hidden very early in the piece.

 I checked the link and there isn't anything there to remove Cortana. All you can do is disable it.

really? This far in to W10 and you would even think about moving back to a system that is falling farther down the support chain? Not logical at all..

And you can upgrade it to 10 for free.

https://www.microsoft.com/en-gb/accessibility/windows10upgrade 

brand new as in couple of year old hardware (pre-skylake) or brand new brand new? because.. you might have heard that ms has stopped providing any sort of patches for win 7 and 8.1 for anything newer than skylake... as well as some skylake machines

https://arstechnica.co.uk/information-technology/2017/04/windows-7-8-old-cpu-updates-blocked/

I have W7 on my machine and it still gets all the patches/updates.

Brand new as in Ryzen 7 1800X, so it will have that issue. And yes I did/do know that will happen in the future. It hasn't as of this time yet though, and of course it isn't like I can't upgrade to win10 at that time. When that time comes I will just have to make a decision; run without updates, upgrade to Win10, or upgrade to Linux. It could be pressure will have caused MS to change their stance on data collection by that time, and Win10 will make good sense then. For now, I'm good. I'll be hurting on games that do Directx12, but not Vulkan at some point. But as of now, I don't run any games that I need to worry about that.

For those who don't know, majorgeeks.com hosts all the patches and updates from MS, meaning that anyone can update any machine, regardless of MS stance on 'new' hardware.

Don't count on it!  MS recently spoke of hard-coding various advertising and data collection tools into the OS using Windows Explorer... and unlike the built-in apps, which can be uninstalled or disabled, those tools cannot be removed or disabled without completely crippling the OS.  It was rumoured they were to have been implemented with the Creator's Update, though I've not heard of anyone with the update complaining thus far.  I've not seen anything like that since updating, either, but MS decided it would go the hard-coded way because data its mining apps could be disabled, and come Hell or high water, they really, really want that data.

And if you have no use for it, why keep it?  I never gave it a chance to be irritating.  Once I'd read that it wants to know the ins and outs of everything one does and where one is, I got rid of it.  Microsoft isn't to be trusted with that much knowledge, and for those who think all this data mining is harmless, and won't affect them, well let's hope it doesn't come back to bite them on the bum.

So, a different question. Instead of removing Cortana, how do I completely disable it?

Yeah, but she's a sneaky bitch!  She'll just go 'round the corner and still listen to everything he says.      

Kona, go into Settings and Privacy.  There you will find means to turn Cortana and other apps off.

I was able to update my new computer successfully, so either they are incorrect, or its a rolling release on that program. I received that Ryzen cpu on the 7th, and assembled/updated on the 8th and 9th.