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>>It took several more years before mathematicians succeeded in even constructing the monster group, but they had a good excuse: The monster has more than 10^53 elements, which is more than the number of atoms in a thousand Earths.

Did they create a set of numbers the size of 10^53 ? That seems impossible since you need more capacity then all atoms of 1000 Earths!




That's not quite what they mean. By "constructed" they mean "demonstrated that it exists and has the specified properties." They didn't write down every element explicitly.


That's right. For example, you can construct the integers Z without writing all of them down. Which would take a long time ...


53! is how many digits base 10? That's the size of the symmetric group on 53 elements. Groups can be exponentially larger than their underlying set.




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