If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and… then that must mean that there are not only infinite infinities, but an infinite number of those infinities. and an infinite number of those infinities. and an infinite number of those infinities. and an infinite number of those infinities, and… (infinitely times. and that infinitely times. and that infinitely times. and that infinitely times. and that infinitely times. and…) continues forever. and that continues forever. and that continues forever. and that continues forever. and that continues forever. and…..(…)…
That there are infinite natural numbers is the central property of infinity
>>16827001Correct.
>>16827001Truths:1: Between any two rational numbers there is an irrational number.2: Between any two irrational numbers there is a rational number.Tiny mind paradox:There are infinitely more irrational numbers than rational numbers
>>16827030>1: Between any two rational numbers there are infinite irrational numbers.>2: Between any two irrational numbers there are infinite rational numbers.If there were just one in between, they'd be the same infinity.
>>16827005N-n-nnoooo!! You can't just make infinitely new numbers out of thin air!
>>16827001He looks like he works at Pizza Hut
>>16827030Correction: there are infinitely more undefinable numbers than definable numbers. Isnt that odd? The numbers that can’t be represented whatsoever… that we don’t even know exist.. are the only reason that “uncountability” exists as a concept. Is it any wonder that you can’t count what can’t be defined? The irrational numbers are countable when restricted to what’s definable.
>>16827093>that we don’t even know existOf course we do. They're all infinite paths in a complete binary tree and if they weren't there, you'd be missing pretty much the whole tree.
>>16827121Prove there exists at least once sequence of decimal digits for which there does not exist a finite definition. Be sure to not rely on circular reasoning in your proof.
>>16827047There'd be at most two of each.
>>16827332Knock yourself outhttps://en.wikipedia.org/wiki/Diagonal_argument
>>16827464The diagonal argument relies on the assumption of both undefinable numbers and undefinable lists. So it’s assuming what it’s trying to prove. That’s circular reasoning. Try again.
>>16827965Your word game today was Agrippa's trilemma. Better luck tomorrow.
>>16827979You ignore the possibility that all so-called undefinable numbers actually have a corresponding finite definition, which would undermine the diagonal argument, because it’s already known that the definable numbers are countable. You have yet to prove that there exists an undefinable number, and you never will, because they cannot be pointed to. They are entirely fictional.
>>16827986>Appeal to constructivismDenied.
>definition has always been a cool thing>infinitely& in that infinite... like infinitely cool.. it's like one of its steps man, what you're talking about is sooo true yo!
>>16827997Reality has a constructivist bias
>>16828022Denied because you're already working with definable numbers.
My favorite thing to do in high school was beat up math nerds. I wish I could've majored in it in college.
>>16828070It's called screenwriting, sorry you missed out.
