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How do we know modern day math is correct?
An example would be one is equal to zero point nine repeating. You can divide them both by three, and get point three repeating, but if you times point three repeating by three you can only get point nine repeating... another question could be, where does the rest of it go?

For the answer to the question about 0.999..., see Question 181 . Mathematicians try to ensure the correctness of math by never accepting a mathematical statement as true without a proof. Of course, it's always possible that a mathematician will make a mistake when writing or checking a proof, so even if a mathematician has proven a statement and the proof has been checked by other mathematicians, there is still a small chance that there is a subtle mistake somewhere in the proof. (It has occasionally happened that flawed mathematical proofs have been accepted for years before someone finally spotted the flaw.) So if you're looking for an absolute guarantee of correctness, I don't think you're going to find one. But even if we ignore the problem of careless errors, there are other questions one could raise about whether or not a proof of a mathematical statement guarantees the correctness of the statement. Usually a proof of one mathematical statement makes use of other mathematical statement...

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