# Field acioms- division

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• November 15th 2007, 04:03 PM
lds09
Field acioms- division
Hello, I need some help on how to prove this using the field axioms of the real numbers

Given a and b with a =/ 0, there is exactly one x such that ax = b. This x is denoted as b/a.

Thanks in advance
• November 15th 2007, 05:21 PM
ThePerfectHacker
Quote:

Originally Posted by lds09
Hello, I need some help on how to prove this using the field axioms of the real numbers

Given a and b with a =/ 0, there is exactly one x such that ax = b. This x is denoted as b/a.

Thanks in advance

$ax=b$ then $a^{-1}(ax)=a^{-1}b$ then $(a^{-1}a)x=a^{-1}b$ thus $1x = a^{-1}b$ thus $x=a^{-1}b$.