Computers are the automation of mathematics. If you can't reduce something to mathematics, you can't make a computer do it.
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No because infinite processes can’t be computed but there are analytical methods in math that can deal with infinities. So computation is a subset of math.
But those methods can and have been implemented on computers, and infinity doesn't exist anyway.
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If infinities don’t exist then a lot of math will have to be reworked.
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Infinity a useful fiction. We don't want to do away with it, just not get confused about what it means.
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