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There's a renowned mathematician called Doron Zeilberger who is arguing that infinity is nothing more than a human construction to make very big numbers calculable.
He's come up with many clever ways to solve problems of infinity and new math to work around it.
I first learned of this some time ago through a Swedish article in a science mag that I'm unable to share.
But here are some sources for you to read at least.
http://www.math.rutgers.edu/~zeilberg/Opinion108.html
http://www.thenakedscientists.com/forum/index.php?topic=48702.0
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