4 ms·
You are wrong! The algebraic field extension ℚ[π] contains π.
by arberavdullahu 7y ago
You are wrong! The algebraic field extension ℚ[π] contains π.
- OscarCunningham 7y agoI think people would normally call that a transcendental extension and not an algebraic one.
- klodolph 7y agoℚ[π] is not an algebraic extension of ℚ.
- jopolous 7y agoI guarantee that is not an algebraic extension. It's not even a finite extension
- lonelappde 7y agoThat's not a valid critique, as other commenters explained
- doomrobo 7y agoFinite implies algebraic. The other comment says that the converse isn't true.
- jopolous 7y agoYou'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