3 ms·
Strictly speaking that property hasn't been proven of pi (nor whether this would still hold for powers of pi). As you may have gathered irrationality is a weake
by contravariant 8y ago
Strictly speaking that property hasn't been proven of pi (nor whether this would still hold for powers of pi). As you may have gathered irrationality is a weaker property.
Irrationality would be enough to guarantee that you can find a power where your name is right at the start. You do need log(pi)/log(10) (or whatever base you're using) to be irrational for that to work, but I think you can prove that using the fact that pi is transcendental.