[jopolous]

I guarantee that is not an algebraic extension.

It's not even a finite extension

[lonelappde]

That's not a valid critique, as other commenters explained

[jopolous]

You're totally right, I could have worded that differently. I actually posted an infinite field extension that is algebraic elsewhere in this thread, but usually those are tricky and I haven't seen them pop up as often as finite algebraic extensions

[doomrobo]

Finite implies algebraic. The other comment says that the converse isn't true.