At some point in my past I became biased towards inequalities over equalities; they somehow seemed more fundamental (I have no intention to defend this sentimen

At some point in my past I became biased towards inequalities over equalities; they somehow seemed more fundamental (I have no intention to defend this sentiment... its probably insubstantial). So there are lots of fun inequalities, but probably my favorite is the bound on the support of eigenvalues of a matrix given by the Gershgorin circle theorem (https://en.wikipedia.org/wiki/Gershgorin_circle_theorem https://en.wikipedia.org/wiki/Gershgorin_circle_theorem).