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How does nest determine outside temperature?
The temperature on your thermostat screen and app is rounded to the nearest 1F. When to turn on your system is determined by the unrounded temperature on your thermostat. Before your system turns on, the temperature on your thermostat or app could change by a few degrees.
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Assume that $E\subset F$ and that $E$ and $F$ are fields. Also, say $[E:F]=p$, where $p$ is a prime. If $a$ is any element of $F\setminus E$. Show that $F=E(a)$.
I'm pretty unsure of how to approach this.
Degrees are multiplicative: $$ [F : E] = [F : E(a)][E(a) : E]. $$ See Proposition 1.20 of Milne's notes for a proof. What can you say about $[E(a) : E]$ now?

source: openbmb/Ultra-FineWeb