I'm not studying algebra yet, I just happened to notice this and am curious. Mathworld's entry for the field axioms doesn't include closure axioms, but I have seen other authors include closure axioms in the field axioms. Does anyone know why this is or what difference it makes? Can closure be deduced from the other axioms?(adsbygoogle = window.adsbygoogle || []).push({});

Without the closure axioms, could you prove, for instance, that the sum and product of a nonzero rational number and an irrational number are irrational? The only way I know how to prove this is with the closure axioms.

**Physics Forums - The Fusion of Science and Community**

# Field axioms with or without closure

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

Have something to add?

- Similar discussions for: Field axioms with or without closure

Loading...

**Physics Forums - The Fusion of Science and Community**