I'm creating the concept for a story called The Little Differences. It's about an accountant that, one day, out of the blue, notices that a certain calculation is producing a slightly wrong result. Barely noticeable, nothing world-changing,

He runs it on the computer, tries different software, a physical calculator... everything gives a result that's a little off. When he checks on paper himself, he gets the correct result. But, to his surprise, everyone else tells him that he's the one that's off, and that the incorrect result is actually perfectly sound.

I need something that makes sense, mathematically. The weird result must be something that really is wrong, and not just something that programs sometimes get wrong (I don't want it to be explained at all... I mean, the reason why it is occurring must not be something easily reducible to some well-known malfunction). But it must also be minor enough for someone to miss, something that wouldn't really cause much trouble in the real world (is that possible? IDK).

Lastly: it must be something that I'm able to explain (on some level) to a non-math reader.

So, Tildes math wizzes, what you suggest? :D

I'm interested in the subject, but don't know where to begin investigating it. I tried to look over the code for SeDuMi, but it is much more massive than I had realized. I have a background in mathematics, if anyone can point me towards a textbook.

Does there exist a function that does not include any trigonometric function in its definition that has similar properties (periodicity, for instance) as trigonometric functions? I can't think of any, and this strikes me as a bit surprising.

Edit: I thought of a simple answer: piecewise functions can achieve this!