/sci/ - Science & Math

Surreals are a fun useless math thing that can't even be handled well (it's not even a set) and has no use in real world or other branches of math.

Infinitesimals can be used to formalize analysis but noone cares.

For infinities, just check out set theory, especially ordinals.

>>6929590
> has no use in real world
Super imposing the natural space of a wavelength into an algorithm while having a CS degree could result in controlled time/space travel

>>6929553
pretty sure surreal numbers were used to study go endgame positions

btw I once played berlekamp in an AGA tournament and beat him

>>6929553
I don't know much about analysis, but in my logic class we have constructed the hyperreals, etc. it is an immediate consequence of the incompleteness theorems that there are other models of arithmetic. we chose to produce them using the ultrapower method (wiki it) which is relatively straightforward. the same method can construct the hyperreals, which by los theorem has the logically very nice transfer property. the ultrafilters themselves used in the construction of the hyperrreals completely emulate taking limits, and infinitesimals can be handled as actual elements. idk or care abt analysis much, but apparently you can do almost all calculus this way algebraically/logically which might be nice given your tastes. it is also apparently good for so-called "epsilon management" and since you don't need all those nasty "for all reals greater than 0" you can do many proofs and computations with many fewer crossing quantifiers.

Google: ultrafilter, ultraproduct, los theorem, hyperrreals, transfer principle, hyperreal analysis

>>6929664
very simply: the ultrapower construction gives you a number which has all first order properties of reals (so can be added, multiplied, etc) but is larger than all other reals. now take its reciprocal.

>>6929668
>>6929664
>>6929649
>>6929608
>>6929590
Thank you, reading up on this stuff is incredibly fascinating. I feel strangly peaceful seeing the complete representation of every possible value in any possible way represented.

Dedekind cuts are also facinating to me