Say you have a dot. That dot explodes into an infinite number of dots. Each of those dots explode into a new infinite number of dots. Each of those dots explode into a new infinite number of dots, ad infinitum.How many dots do you have in total?
>>17084664-1/12
>>17084667Ramanjupan poojeetman really trolled entire generations with this one huh?
>>17084664Enough dots to pay for a night of passionate animalistic sex with your fat whore of a mother. So just the right amount.
>>17084664>Say you have a dot.>How many dots do you have in total?You explicitly started by saying that you have a dot. Clearly by your description, those other things are the subcomponents of a dot.
>>17084664you have 1 very schizophrenic dot
an infinite amount obviously. if all those explosions are the same size, it sounds like youre describing iterating the cartesian product of a given set with itself: N, NxN,NxNxN,..., and the logical conclusion would be the countably infinite product of N with itself. If N is countable, like the natural numbers, the size of the end result is the cardinality of the real number line
>>1708466742
>>170846640 dotsThey all explodeded
>>17084664It depends on the carrying capacity. Those dots will eat up too much real estate forcing us to utilize imaginary real estate with infinite supply and continuous demand. We have infinite dots with analytic continuity in the imaginary world.
>>17084885The only good reply here
>>17084667>implying the reals are the same size as the integersretard
>>17085458>Integers aren't realYou're an idiot.
Unknowable, also dots are one dimensional how can you even split them, as explode implies? OP is just looking for an excuse to dream of a scenario where dots multiply infinitely and occupy the entire universe and particularly its subset Canada, therefore it is likely that he is indian
>>17087557point particles are 0 dimensional
>>17084664Let's say that "[math]\omega°[/math]" is the first set of order in infinity defined in Cantor's set.>an infinite number of dots.1st order of Cantor's.>Each of those dots explode into a new infinite number of dots.2nd order of Cantor's.>Each of those dots explode into a new infinite number of dots3rd order of Cantor's.That would be :[math]\omega°^{\omega°^{\omega°}}[/math]
>>17087856Wut, Latex has fcked up.[math]\omega°^{\omega°^{\omega°}}[/math]
>>17084664does the force of explosion combine any dots?
>>17084664>Connecting the dots.
Vortex Mathematics
>>17084664>How many dots do you have in total?If your construction with the exploding dots is countable, then you have as much numbers as the natural numbers in the end.>>17084885>the size of the end result is the cardinality of the real number lineWhy?You have N, NxN, NxNxN, NxNxNxN and so on. You can count that.This is how you visit each of the sets and take the next one out of them.1. N2. NxN3. N4. NxN5. NxNxN6. N7. NxN8. NxNxN9. NxNxNxN10. N11. NxN12. NxNxN13. NxNxNxN14. NxNxNxNxN15. and so onThis means, you visit every set an infinite amount of time and every one of them is countable.
>>17088238Incorrect. Consider each dot born from an explosion to be a digit of a radix based counting system (with Aleph0 as it's radix, which is ofcourse not usable as a counting system because all integers can be mapped within the first digit, but that's not relevant to the argument), then the successive explosion of dots is akin to a real number expansion between 0 and 1, which means that the number of dots has to atleast be as big as the quantity of the set of Real numbers between 0 and 1 which is equal in quantity to the set of all real numbers, and the radix being Aleph0 accounts for the integral parts, which simply means that the number of dots here = the quantity of the set of all real numbers = Aleph1.
>>17088242I understand your argument, but I don't buy it. You are probably thinking of Cantors diagonalization argument.But we have dots, not numbers.The first explosion is just an endles line of dots (or * here)The second one just a gridWe can associate every * with an element of NxN.See image. Fucking board thinks my post is spam.
>>17088242But, I think you're still right that Nx....xN is not countable.I think I've thought too much of a process that is happening, not the endresult.Elements of Nx...xN can just be interpreted as a real number.
>>17088245The diagonalization argument is not really related or relevant to my argument. My argument simply states that the number of dots has to atleast be able to map every single real number, which are very simply every possibly permutation of aleph0 digits(for any finite radix >= 2) and one period.The diagonization argument also uses this fact to try to enumerate reals and then show how it's impossible, but ultimately none of that is relevant to my argument which only use the result of the diagonalization argument(that reals are more numerous than integers), to establish a lower bound on the number of dots.The second half of my argument (about the Aleph0 radix not accounting to much) is wishy washy and I won't formalize it or verify it atm, but I don't think it elevates it to Aleph2, thus I think it must be Aleph1, aka equal in quantity to the set of reals.
>>17088247>Elements of Nx...xN can just be interpreted as a real number.That's what I said, although I can't say that for 100% certain atm
