🧵 Untitled Thread
Anonymous at Wed, 30 Oct 2024 18:56:02 UTC No. 16456120
If a number cannot be exactly defined in a finite amount of symbols, then it does not exist. If it takes a whole (infinite) universe to list out the digits of a number for a mind to even know which number is being talked about, then that number is useless and practically does not exist in any meaningful sense.
However, the set of definable numbers is countable. Therefore real numbers are countable when you exclude the mystical undefinable numbers that humans will never interact with in a trillion years.
So what can we say about Cantor’s diagonal argument? After all, the diagonal number could theoretically be defined. But it is defined in a different _language_ than the ordinal list of real numbers. If you created a new list including all possible diagonals obtained from this higher language, then you could still obtain new diagonal numbers with an even higher language. And yet, all of these numbers are definable and therefore belong to a countable set.
Problem: if the diagonal argument can keep being applied to the new list, then what shall we say about the list of all definable numbers? What is the higher language that allows the creation of such a list? For if it gave a finite definition, then that diagonal number would necessarily be in the list of all definable numbers. Therefore the process could only work with an infinite definition, which we have already shown is meaningless. Therefore the real numbers are countable and we should waste no more time discussing fantasy nonsense.
Anonymous at Wed, 30 Oct 2024 19:30:05 UTC No. 16456134
But who cares whether numbers "exist" or not? What does it matter that a number does not have the property of being actual or however you want to phrase it, as long as you can make logically coherent arguments using it?
Anonymous at Wed, 30 Oct 2024 19:31:53 UTC No. 16456136
>>16456134
What's the application of logical proofs derived from unreal constructs?
Anonymous at Wed, 30 Oct 2024 20:06:10 UTC No. 16456185
Things I have learned about continuum theory:
The definable numbers do not form a continuum because they are totally disconnected and noncompact.
Therr are diagonalizations of arbitrary lists of definable numbers and the union of D and all of the numbers resulting from diagonalizations is exactly the minimal continuum, R.
Furthermore, there is a bijection between the non-D part of R and the permutations of D. Each way to order the list of every member of D is exactly one of the rest of R.
.
Finally, there is no higher level algorithm to create an algorithm to produce every permutation of D.
Anonymous at Wed, 30 Oct 2024 20:09:53 UTC No. 16456190
>>16456185
Diagonalization is only about number representations and not numbers themselves. Numbers do not need to be expressed in binary or digital strings.
Anonymous at Wed, 30 Oct 2024 20:10:20 UTC No. 16456193
>>16456120
So does [math]\pi[/math] exist or not? I can write it in a finite number of symbols (one), but not a finite number of digits. Make a choice already.
Anonymous at Wed, 30 Oct 2024 20:38:57 UTC No. 16456224
>>16456134
What is even the point of math decoupled from what we can observe?
Anonymous at Wed, 30 Oct 2024 20:44:38 UTC No. 16456231
>>16456120
>If a number cannot be exactly defined in a finite amount of symbols, then it does not exist.
says who
Anonymous at Wed, 30 Oct 2024 20:54:26 UTC No. 16456248
>>16456231
Ask that same question, but to people who say that those numbers do exist
Anonymous at Wed, 30 Oct 2024 20:55:41 UTC No. 16456249
>>16456248
I'm comfortable with thinking things I haven't seen still exist
Anonymous at Wed, 30 Oct 2024 20:56:44 UTC No. 16456251
>>16456120
Just change your numeral system if you dislike infinitely many digits, idiot. 0.1 in binary is an infinite expansion, in ternary, 1/3 becomes 0.1.
Jeeesus don't you frogposters learn anything?
Anonymous at Wed, 30 Oct 2024 21:05:57 UTC No. 16456261
>>16456251
Every number we work with, regardless of how many digits are in its expansion, is definable, idiot.
Anonymous at Wed, 30 Oct 2024 21:48:10 UTC No. 16456296
>>16456261
I never said they weren't, fuckwad
Anonymous at Wed, 30 Oct 2024 21:52:34 UTC No. 16456302
>>16456296
I never mentioned infinite digits in the OP, so your contention makes no sense, retard.
Anonymous at Wed, 30 Oct 2024 22:02:04 UTC No. 16456314
>>16456120
It might take many years to write out the digits that is the length of the universe measured in planck lengths, but that doesn't mean the universe is not that many very small quantity units long.
Like wise, say energy cannot be created or destroyed meaning energy has always existed. How many pico seconds has reality existed for (start counting from before the big bang before that before that before that before that...)
Math symbol short cuts are ingenious and valid (if even they were only developed to talk about grain or something)
That we can write 99999999999^99999999999999999999999
And knowing what we mean by 9.
And knowing what we mean by 9^9
Knowing what we mean by the above.
Anonymous at Wed, 30 Oct 2024 22:11:53 UTC No. 16456324
>>16456314
sarrr, please do not stink up the thread
Anonymous at Wed, 30 Oct 2024 22:17:48 UTC No. 16456333
>>16456324
Respond to the points I made and remove your post or else you are a hypocrit for accusing me of what you are doing when I have provided the grand opposite, in a perfect refutation of op.
Anonymous at Wed, 30 Oct 2024 22:27:06 UTC No. 16456343
>>16456120
>uncomputable numbers are ... le bad
NPC detected, opinion discarded
Anonymous at Wed, 30 Oct 2024 22:35:32 UTC No. 16456350
>>16456333
saaarrrrrrrr, your post has nothing to do with my post saarrrrr
Anonymous at Wed, 30 Oct 2024 23:51:56 UTC No. 16456407
>>16456302
>If a number cannot be exactly defined in a finite amount of symbols, then it does not exist.
>finite amount of symbols
Either you're shit at writing or just plain stupid. Probably both. Let's see what it is by your reply.
Anonymous at Wed, 30 Oct 2024 23:59:19 UTC No. 16456414
>>16456407
it’s pretty obvious what he’s saying, anon. What’s the problem?
Anonymous at Thu, 31 Oct 2024 00:09:18 UTC No. 16456419
>>16456414
So it's both. Okay then.
Anonymous at Thu, 31 Oct 2024 00:14:33 UTC No. 16456422
>>16456419
what a weird way of trying to argue. I know who you voted for
Anonymous at Thu, 31 Oct 2024 05:57:22 UTC No. 16456690
>>16456422
>muh pol
Never post here again, you literal retard.