№2719882[Quote]
>>2719858Thank you for posting this. I forgot to download it from the previous thread
№2719887[Quote]
>>2719869binary system is just a representation, you can infringe on the complex numbers, by first translating into the decimals were everything is well defined and then proving that imaginary numbers exist.
№2719897[Quote]
>>2719876>Yet you are making claims about absolute certainty, which are absolutely rightValid point, but by your logic nobody could make any claims since a claim relies on absolute certainty.
>How does that prove your point? Both of those things are limited, so how could they get absolute certainty?In what sense limited, I agree they have finite properties, but logical conclusions just like the game of monopoly is finite.
№2719905[Quote]
>>2719880>I largely agree but there is no supposing you can literally prove that a system can be free of internal contradictions.proving it has no internal contradictions is easy, only the axioms neednt be contradictory
DISproving it has A contradiction is impossible
>>2719887No, a field is defined by its operations, not its elements.
You start from the smallest possible set and a single operator, and work your way out to expand the set and number of operations, because thats how you ensure you end up with a field without contradictions
If you treat binary numbers just as a representation, you end up with internal contradictions the same way a computer ends up with rounding errors.
This should be pretty important to you if you care about truth.
№2719947[Quote]
>>2719905>DISproving it has A contradiction is impossibleYou can prove this. I think what you want to get at is that you cant prove the axioms are true with certainty.
>No, a field is defined by its operations, not its elements.Wrong a field in the algebraic sense can either have a finite amount of elements or an infinite one, therfore elements also determine the field,
№2719962[Quote]
>>2719947The way you would prove is that you show that in the axioms of first order logic meta statements (statements about statements) are contradiction free.
№2719981[Quote]
>>2719947>Wrong a field in the algebraic sense can either have a finite amount of elements or an infinite one, therfore elements also determine the fieldmakes no actual sense. the set [0,1] using addition and equality expands to integers, then complex numbers
like I've shown the set [0,1] using the NAND operation expands to binary numbers
a field of elements without any operation is meaningless.
№2719987[Quote]
>>2719981I am just saying that operations and elements determine a field not either one exclusively.
№2719991[Quote]
>>2719897>by your logic nobody could make any claims since a claim relies on absolute certainty.No, a claim is a statement about a particular thing. Anyone can say a claim without any certainty and with some certainty
>In what sense limitedLimited in the sense that we can not know everything. We cannot know whether an object will fall to the ground every time if we tested it 9,999,999,999 times because the trials are so numerous and so many factors could prevent the object from falling. From this, I concluded that cannot be absolutely certain about anything
№2720002[Quote]
>>2719987yeah but the amount of elements is totally irrelevant.
№2720014[Quote]
>>2719991>No, a claim is a statement about a particular thing. Anyone can say a claim without any certainty and with some certaintyAnd I am making a claim that there is a way one might be able to proof something with absolute certainty.
>LimitedWell logic is different, when you play monopoly the rules dont change after a certain amount of play throughs.And still if not, I could have proofed for a limited amount of time that something is true with absolute certainty, that is still something that is absolutely certain.
№2720024[Quote]
>>2720002Definitely not in computer science maybe but in math in general it matters very much, since entirely different things apply to finite fields and infinite fields.
№2720036[Quote]
>>2720024how does the finitude of a field determine its operations, exactly?
№2720045[Quote]
>>2720036The one doesnt determine the other, but they both determine a unique kind of field, but the way you extend finite fields is completely different from infinite ones for example.
№2720080[Quote]
>>2720014>logic is different, when you play monopoly the rules dont change after a certain amount of play throughs.How can you be certain that it will always happen, every single time?
№2720085[Quote]
>>2720080Because then it wouldnt be monopoly anymore.
№2720088[Quote]
>>2720085Same with my proof it would then neither disporve or proof my claim.
№2720089[Quote]
>>2720045no but the set being infinite or not says nothing about the operations
>>No, a field is defined by its operations, not its elements.>Wrong a field in the algebraic sense can either have a finite amount of elements or an infinite one, therfore elements also determine the field,again, since you didnt answer the question, how does the finitude of a set prove elements also determine the field?
in the two examples here I could start with a set [A,B] and addition and functionally re-create all integers in terms of A and B
now given the length of the set S=[A, B, A+A, A+B, B+B, A+A+A …] |S| how on earth does the LENGTH of it (|S|) tell you anything about the operations?
the conclusion is correct, but the reasoning is totally absurd
№2720098[Quote]
>>2720089I am not talking about the elemtns themselve since every element can be replaced by another element symbollicaly thus individually they dont determine the field, but elements determine the field in the way that operatiosn have to have certain properties, for example in any finite field the field has characteristic p, which means applying an operation p times to the same element yields 1 (the neutral element).
№2720103[Quote]
>>2720098I meant 0 not 1.
№2720106[Quote]
>>2720088What do you mean?
№2720109[Quote]
>>2720106Since my method of doubt relies on internal logic only, if that logic was changeed it wouldnt be the method of doubt anymore therefore it couldnt make any claims about the method of doubt (or only marginally). Same goes for monopoly if the internal logic was different it wouldnt be monopoly anymore and we could only marginally infringe on the original game.
№2720165[Quote]
>>2720089* how does |S| prove elements of S determine the field?
lets say a field is determined by a set and operand(s)
whether that set is finite doesnt tell you anything about the field (the axioms, elements or operands)
>>2720098>>2720103yeah but 0 and 1 are neutral elements because 1*a=a and 0+a=a, I can create a set of playing cards and make the ace of spades the neutral element
also I'm assuming you're talking about -, for example
we can take a from S, apply a-1 a times and end up with 0
but this requires for any b<a a-b=c where c>0
now if a is the largest element in our set, and 0 the smallest, then the element a+c must exist, which would mean + and - exists, as well as infinite elements
if were working in a finite set Z/aZ (basically the modulo ring of a) then a+c=c-1 -> a=-1 (which is how the binary set from earlier worked) applying a-1 a times will still give me the neutral element
so in this case at least the length tells me nothing
№2720168[Quote]
>>2720109Hmm, you have convinced me that we can have absolute certainty about things that have very limited scopes, such as the rules of monopoly, but when it is applied to things that could be influenced by many factors such as a world beyond us, I am still sceptical
№2720182[Quote]
>>2720168This question is of a very different nature, I never claimed that that I can prove everything with absolute certainty, I only claim that it might be possible to find small islands of truth admits the vast ocean of uncertainty. I believe for example that the physical laws can never be things which we can be 100% certain about.
№2720203[Quote]
>>2720165> how does |S| prove elements of S determine the field?They dont uniquely determine the field but they play a signifikant role in determining the character and thus the overall structure.
>modulo ringmodulo 5 is a field for example, it has characteristic 5 determined by its elements (it has 5 elements).
№2720213[Quote]
>>2720203By characteristic I mean that if you add 1 five times you get 0, of course what you choose as addition and multiplication also matters.
№2720221[Quote]
>>2720165Btw can I ask you, what did/ do you study for you to have this amount of knowledge about fields?
№2720298[Quote]
>>2720182>I never claimed that that I can prove everything with absolute certainty,I thought that we were still debating that, but I was wrong.
>I only claim that it might be possible to find small islands of truth admits the vast ocean of uncertainty.Fair enough. I guess that I was confused about what your point was
№2720324[Quote]
>>2720221electrical engineering
I dont know the formal definitions for a lot of stuff
>>2720203>>2720213yeah but if I have [A,B,C,D,E] I also have five elements, but that tells me nothing about the operations of this set
№2720336[Quote]
>>2720298Well it is fairly obvious that you can never deduce the 'law of gravity from pure logic alone for example, but wasnt the last discussion really about if we can even prove with one thing with certainty and I think we can do that, just as I have mentioned.
№2720337[Quote]
>>2720336ignore the first with
№2720354[Quote]
>>2720324>electrical engineeringsick
>yeah but if I have [A,B,C,D,E] I also have five elements, but that tells me nothing about the operations of this setThere is no field with 6 elements for example, regardless what operation you choose.
№2720399[Quote]
>>2720336>the last discussion really about if we can even prove with one thing with certainty and I think we can do that, just as I have mentioned.Yes, and I agree with you, so that has been resolved
№2720409[Quote]
>>2720354isnt there just Z/6Z?
№2720426[Quote]
>>2720409It isnt a field, just a ring. Because from what I remeber there are euqations in Z/6Z where ab=0 and neither a or b are 0, but a field requires one of them to be 0.
№2720430[Quote]
>>2720399Great!
Do you want do discuss something else then?
№2720448[Quote]
>>2720438Ah btw remember when we talked about Earthbound for N64? I got my facts mixed up, I knew there was a beta for N64 where bits of gameplay survived, but I was mainly talking about SNES earthbound.
№2720459[Quote]
>>2720448I do. Heh
Have you ever played it?
№2720474[Quote]
>>2720459No, but I would only play it if I had a physical SNES copy.
№2720480[Quote]
>>2720474>I would only play it if I had a physical SNES copy.Why?
№2720490[Quote]
>>2720480Because it would be gemmy to have the rare physical SNES copy.
№2720497[Quote]
>>2720490Why not use an emulator?
№2720502[Quote]
>>2720497I want to have a physical copy of the game.
№2720538[Quote]
Okay I will go to sleep now. Good night!
№2720543[Quote]
>>2720502It's so expensive… it's not worth it
I played it on an emulator until I got stuck fighting the boss in magicant and gave up. I had mixed feelings about it because took so much time to play and it required external information to complete (the player was supposed to use a giant player's guide that came with the game to solve), that made the game less fun for me. Recently I have had been reminiscing about the game because the story and environment is so memorable and warming. It defines what makes life good
Playing it requires a long commitment that I did not have on my first run, but it is worth it
№2720550[Quote]
>>2720543Maybe I will try it some time if I get to it.
№2720557[Quote]
>>2720538Good night Rolf. Make another thread like this if you ever have deep thoughts again
>>2720550Great!
№2720559[Quote]
>>2720557I will definitely do it if something interesting comes to my mind.