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Using Table and ignoring all errors and warnings?


I would like to use Table function, but have it ignore any errors or warnings and skip that value if one is produced.

Illustrative Example:

Table[1/i, {i, -3, 2}]
Power::infy: Infinite expression 1/0 encountered. >>
{-(1/3), -(1/2), -1, ComplexInfinity, 1, 1/2}

I would like the output to just be

{-(1/3), -(1/2), -1, 1, 1/2}

with no errors/warnings given as messages and the index that would produce a message to just be ignored. It's not just specific to 1/0 error, but any type of error or warning I want it to ignore it and skip to the next value; with the final output being a list of valid answers according to expr.

Is there a way to do that? Thanks!



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