Should nits be picked?

I suspect most authors get emails from readers that cause an initial surge of pleasure, followed by a sense of anxiety. They tend to have the format 'I am enjoying your book...' Good! '... but...'  Ah.

I've just had the first of these for my new book Are Numbers Real and I wanted to share it, to consider whether sending this sort of email is a good idea or not.

My correspondent, Harvey Randall, started by saying he was enjoying the book, so I got my initial positive peak, but then he pointed out
However, there may be either a non sequitur or a typo on page 24...
The first line on the page, continuing the sentence on the previous page, states "... a simple rule) to add XXIII to XLIV for instance ... teach children how to add 23 to 45 ...."
I believe XLIV = Arabic 44.
While there is no particular reason why the Roman and Arabic sums should have been the same one, so it's not strictly a non-sequitur, I suspect with the numbers so close it was a typo (I honestly can't remember what I intended), and I have requested a change for future printings.

On the one hand, then, this is a useful thing to do. It's good that we can correct the typo (though obviously nothing can be done for existing books in print), because errors distract some readers from the content, and though this particular one does not alter the message in any way, anything that causes a distraction weakens the book.

Now, every book I've ever read contains typos and errors - I always spot at least one, but I don't usually contact the author to tell them. (If I'm reviewing a book I do as a courtesy, but that's a bit different.) I think there are two reasons for this. One is I don't want to impose the same sickening drop of the stomach on discovering an error on another author - and the other is I think it makes me look a bit of a nit-picker. To be fair, anyone who knows me realises I am, like many with a scientific background, a serious nit-picker anyway, so perhaps this shouldn't bother me.

I don't think there is a cut and dried answer. I'm certainly not asking readers to stop pointing out errors - I always pass them on to the publisher (though I'm not sure the publisher always does anything with them), and I genuinely want my books to be as good as possible. But they aren't very nice emails to receive.

So if you do pick up a copy of  Are Numbers Real, which I hope you will - it's taken off in the US faster than anything else I've written, and we'll have a UK edition in about three weeks' time (available for preorder) - please do feel free to point out any errors (though not this one). I will genuinely be grateful, if also a little sad.