4 ms·
>>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
by 31reasons 12y ago
>>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!
- AngrySkillzz 12y agoThat'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.
- wilsynet 12y agoThat's right. For example, you can construct the integers Z without writing all of them down. Which would take a long time ...
- crb002 12y ago53! 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.