Infinity is more complex than you might think
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A new kind of infinity appears to break the rules of how extremely large numbers behave, and could redraw the way the mathematical universe is ordered.
It may come as a surprise, but mathematicians have long known that there is more than one kind of infinity. In 1878, Gregor Cantor first showed that the infinite set of real numbers, which includes negatives and decimals, is actually larger than the infinite set of natural, or whole, numbers. Proving this involves a careful comparison between the two sets, rather…