All Questions
2
questions
1
vote
1
answer
91
views
Alternative to the proof on Wolfram Mathworld that $\mathbb Q$ is the smallest subfield of $\mathbb R$
Exercise 2 (b) on page 100 of Analysis I by Amann and Escher asks me to show that $\mathbb Q$ is the smallest subfield of $\mathbb R$.
Wolfram MathWorld gives the following reasoning:
I don't know ...
9
votes
2
answers
1k
views
Proving (without using complex numbers) that a real polynomial has a quadratic factor
The Fundamental Theorem of Algebra tells us that any polynomial with real coefficients can be written as a product of linear factors over $\mathbb{C}$. If we don't want to use $\mathbb{C}$, the best ...