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I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis ... ... and I am also referencing concepts in Derek Goldrei's book, "Classic Set Theory for Guided Independent Study" ...

I am currently focused on Garling's Section 1.3 Relations and Partial Orders ... ...

Garling defines a partial order as follows:

... ... BUT Goldrei's definition is (apparently) slightly different ... as follows:

Can anyone explain why Goldrei includes reflexivity but Garling doesn't ... ... ?

Is it because reflexivity can be derived somehow from Garling's condition (ii) ... which appears to simply be anti-symmetry ... ?

Can someone please clarify this issue ...

Help will be appreciated ...

Peter

I am currently focused on Garling's Section 1.3 Relations and Partial Orders ... ...

Garling defines a partial order as follows:

... ... BUT Goldrei's definition is (apparently) slightly different ... as follows:

Can anyone explain why Goldrei includes reflexivity but Garling doesn't ... ... ?

Is it because reflexivity can be derived somehow from Garling's condition (ii) ... which appears to simply be anti-symmetry ... ?

Can someone please clarify this issue ...

Help will be appreciated ...

Peter