Thanks for the extensive comment, I agree with you!

However, the project should be viewed from a programmer's perspective, not from a mathematician's. In my opinion the encoding fits the task of approximating specific real and complex numbers good enough, while still being minimal and easy to understand.

For me it doesn't matter that one could encode functions that are not real or paradoxical, not permitting this was never the intention. I improved the wording in the article a bit to make this more obvious.

I do like your idea with the integer pair though, I may try that out in the future :)