Suppose we're in a field F in which x,y,z are members. Consider the axiom of distribution which states that(adsbygoogle = window.adsbygoogle || []).push({});

xy + xz = x(y + z) for all x,y,z ∈ F.

Now consider this deduction:

xy + xz - xy ⟹ xy + x(z-y)

True no doubt, but to check my understanding aren't we missing a step? Shouldn't we more accurately say:

xy + xz - xy ⟹xy + xz + x(-y)⟹ xy + x(z-y)

I'm trying to self-study Rudin and just want to check my understanding.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Distributive Law in a Field

**Physics Forums | Science Articles, Homework Help, Discussion**