Re: Log i = 0

Le 25/05/2025 à 17:50, sobriquet a écrit :

Op 25/05/2025 om 16:58 schreef efji:

Le 25/05/2025 à 15:02, sobriquet a écrit :

There is no certainty in math. But when you encounter conflicting claims

>
Well, that's exactly the opposite :)
There is nothing but certainties in math, since everything is proved in a non-discutable way.

 Not really.. for instance, there are people who reject proofs by contradiction, so some proofs might be acceptable to some while being rejected by others.
Also, things that used to be considered obviously true, like the shortest distance between two points being a straight line have later become uncertain (with the potential curvature of geometry as opposed to flat geometry).
And there is evidence that we can't even have a completely reliable system where we can prove everything that is true and nothing that is false, since Gödel has shown that any formal system that includes basic arithmetic must necessarily be incomplete.

Well, that's true about Gödel's theorem: it says that there exists some propositions that cannot be proven true or false. It does not imply that what is proved can be "uncertain"!
In practice, what we call "maths" in 2025 is totally proved in a rigorous way, with the proper hypothesis clearly given. The famous example of the "straight line" is historical and is related to a period of time where the logical basis of maths where not strongly established. We are not in the XIX's century any more!
99.9999% of mathematicians accept the proofs by contradiction,
and I really wonder what is the point of the remaining 0.0001% :)
--
F.J.