yep  last night were like: 

i got upat 2:30 and couldnt fall asleep then thought lets code coding. 


then later tried to fall asleep with watching space documentaries. 

 


but then usually everytime i fall asleep at 5th minute latest anytime i watch a science documentary whilst resting.  (everytime i watch either a sci fi show or a science documentary I fall asleep like that when resting condition i when watching i fall asleep) 


so same thing i did last night when got after 2:30.  i opent sci fi documentaries. at the same time knowing i would fall asleep 5 minutes later since same happens every day. but the documentary told universe is infinite  then i got fixated to revisiting rethinking infinity concept alike and revisited cantor's diagonalization lemma to have a refutation mindset against it. although might be wrong on that either. 

then i have to revisit studying to grp topics and such also. but i think even with forgotten some such topics, i had some idea about kernels based depictipon of cardinality indexing theorems. that quotient groups thingy of kernels thingy. i think thats how to index to N is indeed. and then the infinity then becomes i mean more divergent shape of infinity is then where kernel size is infinite indeed.  


i think thats like in category theory natural isomorphims concept.  since there is only one such set indeed.  i mean among shapes of infinity this shape is conceptually unique but still could be extended to many mappings based more infinite. but the basic induction layer of that grp is unique infinity shape.


so i had some refutatory idea against cantor's lemma on that aspect that the diagonal wouldc also be generated by the generated natural numbers index in that. so yep there exists shapes of infinity but cantor's diagonalization is idea wise no single infinity shape is  correct but algorithm wise not exact. i think since by than abstract algebra were not this much developed so cantor used computer science method alike some inductive thinking in that.


but more definitive thing of different shapes of infinity concept could be alike : 

 i think its all about mappings and there its all about the kernel concept the ultimate divergent shape of infinity is infinity type whuich kernel size is infinite and then but there also some additional infinity shape could be added to that from quotient side either. 

but then the unique infinite kernel size shape could be some unique infinity shape.


but then the quotient there could also go infinitely many then that would be also some quotient wise added infinity which could be again conceptualized by any kernel concept. 


so there is then as an inductive step this type infinities.  (for what were in times where abstract maths were not avail, defined as noncountable infinity by computer science alike inductive methods of defining different types of infinity by before times where abstract algebra hadnt existed) 


first infinite --> 

kernel cardinality finite. 


second -->


kernel cardinality infinite and no quotient


third


kernel cardinality infinite aqnd finite quotient


fourth 

kernel cardinality infinite and quotient infinite  but with finite kernel size for quotient


fifht 

kernel cardinality infinite and quotient infinite but as recursion inductive defintiion of infinity goes to quotient here 


so there is i think this type infinity concepts.


so among infinity discussipons there is this thing:


kernel cardinality and quotient cardinality  


but the basic infinity indicator is kernel cardinality first --> mapper to N


then the kernel cardinality infinity is such shapes:  either in kernel cardinality is finite  or infinite


thats the latter is the thing which is like multiplies infinity with infinity concept 


so these shapes could be also category theoreitcally defined or even grouop theoreitcally defined to conceptualize all different types of infinity as grp mappings. 


so i fixated to this topic last night and thought these later of that indeed shapes of infinity could be defined very definitively and there is actually some templates of shapes of infinity indeed in abstract algebra side. 

and i think to do maths based on such diagrams is more intuitive (as alike intiutionitistic maths type maths). 

i mean where numbers are defined as diagrams either category diagrams of intuitionistic maths or grp diagrams when grps suffice to conceptualize a concept e.g. in this case infinity types concept which i fixated to last night 


so i would go reapply maths analysis concepts to diagrams based defined concepts and even integrator would be a diagram where numbers instead would turn to either grp definitions/mappings concepts or such definitions. 


thats how ml algos would do maths -> any equation defined in intuitionistic maths diagrams with abstract maths. and representation theory either. since i think these are 2 most significant concepts of abstract maths. 






 


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