Re: [math-fun] Existence from parity

On 30/01/2020 23:16, Cris Moore via math-fun wrote:

This is too easy, but one could also consider the fact that any polynomial of odd degree (and real coefficients) has at least one real root...

Is there a parity-based proof of that that isn't strictly inferior to "f(-large) and f(+large) are large and of opposite sign, so by the intermediate value theorem there's a root somewhere between"? -- g