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Are you talking about Liouville numbers? Liouville numbers are numbers which can be "best approximated by rational numbers" in a certain sense. A number x is
by klodolph 4y ago
Are you talking about Liouville numbers?
Liouville numbers are numbers which can be "best approximated by rational numbers" in a certain sense.
A number x is a Liouville number if for every integer n>0, there exist integers (p,q) such that 0<|x-p/q|<1/q^n
No algebraic numbers have this property, therefore all of the Liouville numbers are transcendental. However! The reverse is not true; not all transcendental numbers are Liouville. Neither pi nor e are Liouville numbers.
- akomtu 4y agoLiouville-ness is a very strict requirement. Instead, we can define "K-liouville numbers, that for all n < K have this property", and then pi is at least a 3-liouville number, which is pretty good.
- klodolph 4y agoIs this the irrationality measure? https://mathworld.wolfram.com/IrrationalityMeasure.html https://mathworld.wolfram.com/IrrationalityMeasure.html I don't think the value for pi is known. The value for e is 2, which is the same value for e.g. sqrt 2.