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ZeroQ[expr] returns True if built-in transformations allow it to be determined that expr is numerically equal to zero, and returns False otherwise.
ZeroQ uses a combination of symbolic transformations and randomized numerical evaluation.
If ZeroQ[expr] returns False it does not necessarily mean that expr is mathematically not equal to zero; all it means is that built-in transformations did not allow this to be determined.
See also: ImpliesQ.