I thought this was a very good way of looking to illustrate why he WOULD think the 20th. Since the ticket indicates days, not parts of days, lets look at your carpentry example assuming full inches, just like the full days on the ticket. Suppose you do need a board 24 1/2 inches long. I hope the clerk at the lumber yard would cut it at 25 inches instead of going back to the 24 inches for your sake. Perhaps it's your carpentry that we should worry about.
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What money was the OP out, by not being able to get into the park that 7th day? Isn't it about $2/ticket for that 7th day? Then he really only lost some face (embarassment at the sloppy math) and about $6. I feel bad if the kids thought they were getting to hit the parks again, and then didn't, but I would have tried to politely explain and hope for pixie dust at guest services....then, failing that, would have bribed my kids with a day in DTD. Kids like souvenirs and Goofys Candy Co!
That said, I very carefully count out our park days on a calendar so that I don't do "Quick math" that might get me in trouble. Really...last day in WDW 20th, first day 6th. If your mind's calculator goes in overdrive and thinks it out too quickly, you automatically might think: 20-6=14!
Having had an awful WDW resort experience myself in the past (which DISers were VERY supportive of, Thanks guys

), I am pretty sure the examples given in this trip report (remember, there might have been more, that was left out for brevity's sake) would NOT have caused me to make a fuss. I hope the OP gives WDW another shot. We did, we were very nervous, but we did NOT regret it!
Beth