u/nip_dip

I am aware that by the Abel-Ruffini Theorem, there is no general quintic formula that could be expressed with an algebraic expression. However, I was wondering if this could be possible with tetration instead.

Tetration, as far as I know, is one of those things in math that doesn't really have any applications. But I was thinking that since tetration's inverse, the super-root, might not be algebraic, maybe they could be used to create a general formula for quintic and higher-order polynomials. Could this theoretically be used, and if not, why not?

EDIT - Tetration is algebraic since it's just repeated exponentiation. I still don't think the super-root is algebraic though.

The day before Fort Sumter, the modern US army replaces the Union army of old. They do not initially control any of the territories occupied by the South, but besides that, they are identical to the modern US military. Those that are stationed in the South or overseas suddenly find themselves on the northern side, so no troops are lost. No nukes are allowed. The US military knows the circumstances they are in, so they will attempt to ensure that there are no Union casualties. Can they defeat the Confederacy without a single Union casualty? Only casualties within the US military are counted, not civilian casualties.

Round 1 - The Confederacy does not initially know the win condition.

Round 2 - The Confederacy knows the win condition.