Skepdick wrote: ↑Sat Jan 14, 2023 9:04 pm
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
Saying the Reals are not listable (in their infinity), is like saying a
square circle is not a shape that can be drawn, but that is because it's not a fricking shape at all!!
Idiot. Do you understand that the natural numbers are in fact listable (in their infinity)?
List 0.
List the next number.
And the next.
And the next...
Now, obviously you don't have infinite time but IF you had infinite time you would be able to list all natural numbers. So then in principle - you can.
Your procedure for listing "all the reals" doesn't work. Because while you are busy listing 0.0 and 0.00 and 0.000 and 0.0000 you NEVER actually get to listing 1.0 and 1.00 and 1.000. So even IF you had infinite time - your procedure fails.
Oh... and
here is your square circle..
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
It's the same here, of course I cannot list undefined numbers, because what the heck is the undefined number? That is not a number! How can I list "things" that are undefined? What is it exactly that I am supposed to be listing???
List the definition? For each number?
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
An infinite "number", is not a number at all. To say it is, would be to go against the law of identity, and the law of non-contradiction. An infinite number never concludes to a "thing", a "something", you cannot tell me to make a list of non-things. It's ridiculous!
Nobody is saying anything like what you are misunderstanding.
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
Yes, I understand that, that is exactly what
can be listed. You can list the finite representation of an infinite algorithm, but not the infinity itself.
What do you mean? The finite representation of infinity itself is the symbol "∞". Obviously I can't show you infinity itself because the concept is in my head. So you'll have to settle for the representation.
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
By asking me to list one Real number, and then another Real after that in such a way that there is no Real in between, is asking me to list the infinities themselves. This is like asking me to paint a picture without paint; you are asking me to make a list without defined number units!
It's nothing like that.
I can run the algorithm for genrating the Natural numbers in my head.
I can't run your algorithm for producing the Real numbers in my head.
Your algorithm never even gets to 1.
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
You are contradicting yourself, the word "number" by definition is discrete. When you say Pi is an irrational number, it's not actually a
number in itself, it's a collection of numbers that can be created by a function based on finite rules and starting values.
You are contradicting yourself. Functions don't generate numbers. They generate representations of numbers. Any function which generates pi to an arbitrary precision is a representation of pi.
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
The fact is, any number you can think of, will be on my list at some point.
The number 1 will never be on your list. And 2. And 3. etc. etc. Your algorithm only enumerates
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
Any level of precision you can define will be included, and you can also use the numbers themselves to represent functions and algorithms that output an infinite stream of numbers and precision. Anything that is a "thing" can be listed, but I cannot list undefinable non-things.
And all the stuff you generate will have smaller cardinality than the Real numbers.
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
Infinities are not
things, get that in your head.
Nobody says they are
things? They are concepts. And they are already in my head...
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
You have never experienced or known an infinity in your life.
I have experienced; and know every single concept in my head. Including the concept of infinity.
Perhaps the word really triggers your sensibilities? If you don't like the word "infinite", then use the phrase "not finite".
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
When you tell me to list the infinitely precise units themselves, one after the other, you are not talking about anything at all, you are speaking gibberish.
Inability to understanding on your part does not imply gibberish on my part.
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
Saying the Reals in their infinite precision are not listable like saying that the set of
non-shapes shapes is not listable, Well yeah, but that is because "
non-shapes shapes" is nonsense! it's not real!
That's a terrible analogy. The set of Reals is not empty. The set of non-shape shapes is empty.
Magnolia5275 wrote: ↑Sat Jan 14, 2023 8:01 pm
When we say "Real numbers" we can only be referring to actual
defined numbers or a function, , and my list will list all that is real by increasing the size of each informational space after the compilation of the previous informational space.
We who? How many voices are there in your head?
When I say "Real numbers" I am talking about the concept of the Real numbers. Nothing to do with definitions.
Of course, there's a couple of different ways to characterise the relevant structure on R, but once you figure out which properties you care about - you can automatically compute a description of its computational representaton.
https://math.andrej.com/2008/02/06/repr ... able-sets/
Your procedure for listing "all the reals" doesn't work. Because while you are busy listing 0.0 and 0.00 and 0.000 and 0.0000 you NEVER actually get to listing 1.0 and 1.00 and 1.000. So even IF you had infinite time - your procedure fails.
You completely didn't understand how my procedure works. When I say you start with a box of 0.0, I mean you first list all the options in the box of 0.0, before going on to the next box of 00.00. So if we start with 0.0, we will get to 1.0:
0.0
0.1
0.2
.
...
0.9
*1.0*
1.1
1.2
1.3
.
...
1.9
2.0
2.1
.
...
9.9
Box of 0.0 finished!
And now we move on to the
box of [00.00]
00.00
00.01
.
...
00.99
...
99.99
(Done! And now we move the decimal point...)
0.000
0.001
.
...
9.999
(and again we move the decimal point...)
000.0
000.9
.
...
999.9
And that is it! We finished all the
finite possibilities of box: [00.00]! Now we move on to the
next box of [000.000] and after that, we go to [0000.0000], and so on, and so on.
As you can see, my procedure covers all the possibilities. Any number you can think of will be listed at some point. When you say I don't get to 1.0, you are simply lying, it does! It reaches that in the first informational box of two zeros: [0.0]
I am aware that my list has repetitions of the same numbers like 000.9 and 0.9, but you can simply not list the repetitions, and in principle, you can have a one-to-one correspondence.
So let's play a really simple game. You are claiming that my method doesn't list all the Reals. So give me any Real you can think of, and I will tell you which information box contains the number you chose. I guarantee you I will have an answer for any number you can think of. This will prove that my list contains all the numbers of any kind!!
Idiot. Do you understand that the natural numbers are in fact listable (in their infinity)?
Idiot, you don't understand what I was referring to. I'm not talking about listing a non-ending list of finite numbers. What I am saying is that you cannot make a list of infinite numbers, which is: 0.3333333333......, I can list 0.3 and 0.33, but not 0.3333333.... because that is not anything real at all! Only the finite fraction "1/3" which can be represented with finite numbers is listable but not 0.333333333...., but yes:
"0.33333333333..." as a finite text that references the finite concept of dividing a decimal unit by 3.
Again, in case you have missed the point, The assertion that I must list the Reals (in their infinite precision)
one after the other, Is the assertion that I must actually list the infinities themselves. There is no "infinite precision" that comes after another "infinite precision" because "infinite precision" does not reference anything in its totality, it's not units, it's nothing at all. The "Reals", cannot be the collection of "
nothingnesses"; nothingness does not exist, only "
somethingness" exists, and I can list all the "
somethingnesses".
That said, my list does go through every single precision space, and since it is never ending, the list itself will contain every level of precision all the way to infinity. So ALL the Reals or contained in my list. Go ahead test me! Tall me which Real is not on my list! I don't care that you call me an idiot, but to say my list doesn't work is just rude! I feel personally insulted when you say that!
"But there is no "smallest" number after the decimal point."
_______________________
Of course there is. 0.000...
When do you reach the 1 at the end of infinity? If you reach it, is that the
end of infinity? A calculation that never ends outputs ZERO results. If A
never = B, then A does
NOT = B. Who is the idiot now? Even the mountain sheep in Alaska know that! lol
----------------------------------------
(edit)
Here is an example of an irrational number whose
representation is listed in my method:
√5
Binary number representation:
11100010 10001000 10011010 00110101
Conversion to decimal:
3800603189
Box_20_zeros >>> [0000000000.0000000000] >> [3800603189.0000000000]
Even my goldfish knows how to do that!
(edit2)
OMG! Even this whole response itself (not including this edit) is on my list!
I am on the list!
010110010110111101110101001000000110001101101111011011010111000001101100011001010111010001100101011011000111100100100000011001000110100101100100011011100010011101110100001000000111010101101110011001000110010101110010011100110111010001100001011011100110010000100000011010000110111101110111001000000110110101111001001000000111000001110010011011110110001101100101011001000111010101
... 111001100100000011010000110111101110111001000000111010001101111001000000110010001101111001000000111010001101000011000010111010000100001
Converted to decimal:
1452971614802563820723241451379142052817369169460541620201783505577485737832
... 4504777469147428680109345599553975462573093365001835072831179566584567145857370765128676085163699312144275258569761
Number of digits: "9183"*2 = 18366
Box_18366_zeros >> [00000... 00.00 ...00000] >>> [145297161480256382072324145137914... 75258569761
.00 ...00000]
It has been destined all along! The universe agrees with me! I know I was right!