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letamp;#39;s talk about ordered fields now weamp;#39;ve talked about fields so Iamp;#39;m taking a field F and weamp;#39;ve actually talked about ordered sets so weamp;#39;ll say F is a field in fact an ordered field if and Here I am assuming that simply the set F is an ordered set so f is just an ordered set but moreover that F is an ordered field if these two things these are the real two conditions if we have three elements here XY and z in F take any three elements well then X less than Y and remember here the less than sign this is our relation this is our ordered relation and itamp;#39;s one that youamp;#39;re probably very familiar with X less than Y well this would imply that X plus Z is less than y plus Z we can add to both sides of an inequality very convenient definitely something youamp;#39;d like to do and then number two here second second part of the definition of an ordered field if we have two elements x and y in F which are both positive so X is greater than z
