Half Blood...Pure Blood????

[mirely_r]

No: HPFGUIDX 67694

Everyone keeps mentioning that Harry is considered half blood 
because Lily's parents were muggles and Jame's parents were pure 
blood.  However if Lily is a witch and James is a wizard would that 
not make Harry pure blood.  Does this just continue to follow his 
decendents to the end of time...at one point does it not convert to 
pureblood???