Quote Originally Posted by Annalise28
Is it possible? Because, if you are the descendant of a witch or wizard, aren't you a half blood, no matter who you marry? Unless you are a squib, of course.
"Half-blood" = one Muggle parent, one wizard parent.
"Squib" = one or two wizard parents, but not a wizard oneself.

There isn't really a definition given in the books for what you would call, say, Harry, who is the child of a pureblood and a Muggle-born. It's hard to use traditional categories of heritage (like "1/4 wizard") because wizardry really behaves more like a recessive genetic trait than a race/ethnicity. (You can't be born Italian if neither of your parents were Italian, for example.) But wizards treat it the way Muggles treat racial heritage. Which suggests wizards don't understand genetics much better than Rowling does.

This makes me think further, though. Because, if all of the wizards/witches reproduced, then we would have a lot of magical children, wouldn't we.
If all of them did, sure. All members of any group don't reproduce, though. We don't know what the wizarding birth rate is. The best guess is that it's similar to that of the Muggles they live with.