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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: Log i = 0
Date: Mon, 26 May 2025 16:36:21 +0200
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On 25.05.2025 19:03, efji wrote:
> Le 25/05/2025 à 18:17, sobriquet a écrit :
>> Op 25/05/2025 om 18:03 schreef efji:
>>> 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% :)
>>>
>>
>> But the same holds for science. It's reasonable to assume that theories
>> like evolution are proven beyond reasonable doubt, but philosophically 
>> speaking, there is no certainty in science.
> 
> Yes, there is no certainty in science, EXCEPT in maths !
> Take any maths book or article, take any proposition entitled "Theorem", 
> you know that it is true forever, without any doubt and without any 
> chance that somebody in 1000 years in the future could disprove it, 
> whatever "science" will be at this time.

That is wrong. Present mathematics simply assumes that all natural 
numbers can be used for counting. But that is wrong.

Regards, WM
> 
>