/sci/ - Science & Math

>>15125231
Indeed, which is why Set Theory, and the principle of the least upper bound forming the basis of the real numbers is indeed, on trail

on trail

on trial

on trail

>>15090505
>>15090541
I say let this anon be correct, and relegate mathematics to the bachelors of arts degrees on par with economics, art history and gender studies

and form a new field called computorics that deals with mathematics in science

>>15079102
indeed, set theory is, indeed, on trail

>>15043504
I'd attest that code quality would improve if programmers started on Wildberger, we take too much for granted in the not-so-real real number system

>>15031091

there is an archive link is this but manages to keep the unrendred LaTeX but the system thinks its spam

https://web.maths.unsw.edu.au/~norman/views2.htm

under "Does mathematics require axioms?"

>Mathematics does not require `Axioms'. The job of a pure mathematician is not to build some elaborate castle in the sky, and to proclaim that it stands up on the strength of some arbitrarily chosen assumptions. The job is to investigate the mathematical reality of the world in which we live. For this, no assumptions are necessary. Careful observation is necessary, clear definitions are necessary, and correct use of language and logic are necessary. But at no point does one need to start invoking the existence of objects or procedures that we cannot see, specify, or implement.

Wildberger first challenges whether the axioms stated are even axioms by definition, than concludes that, even as definitions they are uncomprehendable and hide all sorts of logical inconsistencies. He than concludes that Euclids definition, that if anything they should be self evident truths any novice can intuitively grasp, as an appropriate location to leave the grammatical object 'axiom'

So i suppose if i had to shove axioms in wildbergers mouth it they would be the axioms of mathematical earnestness and humility
1) you've never heard, smelt, tasted, felt or seen an infinite object
2) you've never divided something into an infinitessimal amount either
3) precision at iteration is not a 1:1 substitute for exactness

>>14746102
I'm fine with all maths presented here

just the abstractions to language from the maths i find troublesome. To interpret this equation as one as 'there is only one was to arrange nothingness' as an assumption upon the continuum that is ill thought. Nothingness cannot be arranged. Pointers to null in memory can be however