This is something that I have some time thinking, when can one be sure that a proof one has written is enough rigurous that everybody else (or mostly everyone) considers it valid?

Example:

Theorem "A"

Every polynomial

of a single variable of odd degree has at last one real root

Proof

As

is odd, if

clearly

and

because for

the term with the n exponential grows 'faster' than those of less degree. (1)

If

it justs swaps

with

in the limits above.

And because

is continuous (2) for all x (for been a polynomial), then it has to cross the x-axis at last once (3), so a real root exists.

Of course, points (1), (2), and (3) could be developed further (they asume other proofs that I ommited, call them proof "B", "C", and "D"), but should one add those proofs in order for theorem "A" be complete? Could I only give bibliography where those proofs can be found?

In general, do you think I really proved Theorem "A" above? (I think most will say no)

Thanks,

Damián.