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I think you are on the right lines, in that including contradictions is a good way of indicating that the person is not telling the truth. Of course, you need to avoid the danger that readers think...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/5614 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
I think you are on the right lines, in that including contradictions is a good way of indicating that the person is not telling the truth. Of course, you need to avoid the danger that readers think you are just being sloppy. I think the speaker needs to be caught in a lie - realise that they have said something contradictory. What is more difficult is identifying what they are lying about - that is, when they are lying, and when they are telling the truth. You may need another character to verify important facts (like the eidetic memory, if this is important). It is difficult, because the reader tends to trust the narrator.