Skepdick wrote: ↑Mon Jan 16, 2023 7:50 am
Magnolia5275 wrote: ↑Sun Jan 15, 2023 10:42 pm
Seriously?? So now the problem is that I am listing things twice??
Yes. Precisely. You are listing natural numbers
twice or more. Because
once isn't enough.
Magnolia5275 wrote: ↑Sun Jan 15, 2023 10:42 pm
Didn't you claim the Reals were "larger" than the naturals?
I did, and you are literally demonstrating it!
By having to list the same natural number
twice or more just to accommodate a few Reals.
Magnolia5275 wrote: ↑Sun Jan 15, 2023 10:42 pm
If I am showing you the Reals can not only fit inside the naturals, but some of them can even appear multiple times over, what the heck is the problem? Can you admit then that the infinity of N is the same as R?
You have absolutely no comprehension of what it is that you are even showing.
The situation is so sad you have it backwards. You keep demonstrating that ANY GIVEN real number can be mapped to a natural number. And you keep demonstrating that some natural numbers can be mapped to multiple real numbers. Do you actually comprehend the difference between an injective, bijective and surjective map?
What you continue to fail to demonstrate that EVERY Real numbers can be mapped to unique natural number. What you fail to demonstrate is a bijective map between R and N.
https://en.wikipedia.org/wiki/Bijection ... surjection
Yes. Precisely. You are listing natural numbers twice or more. Because once isn't enough.
You have absolutely no comprehension, I'm not listing naturals "twice", what are you saying? That my list goes 1,2,3,4,4,4,4,5,6,6,6,7,7,8,8? Are you trolling me? What are you talking about?
What may be listed twice is the Reals, but "may" doesn't means you "must", just
once is enough, there is nothing in my method that says you have to list the Reals multiple times, you can
skip the duplicated! Just don't include them when you get to them. Have the algorithm take as input all the previous boxes so it can skip listing the duplicates.
All I said about the list, is that in its simple form, it will list the Reals multiple times in the list, You don't have to do that, you can just skip the duplicates and not list them!
Regardless, this is irrelevant, you cannot claim that a surjection (which has no necessity of even being on my list, you can SKIP DUPLICATES!) Is some obstacle in disproving the claim that the R > N. If anything, it shows just how easily R fits into N, so much so, that it can fit multiple times over! It's like if you with a group of 100 people came to a hotel, and the manager said that not only does he have room for everyone, he has room for everyone multiple times over, everyone can have multiple rooms for themselves. It's the same here, the Reals can have multiple "rooms" in the naturals "hotel" tower.
https://en.wikipedia.org/wiki/File:Surjection.svg
As you can see from the picture, in this case, N would be the X, and Y would be the Reals I am listing. What in the world is the problem? In the picture it shows Y as smaller than X, how can you use that to claim my list cannot include all the Reals?
The situation is so sad you have it backwards. You keep demonstrating that ANY GIVEN real number can be mapped to a natural number. And you keep demonstrating that some natural numbers can be mapped to multiple real numbers. Do you actually comprehend the difference between an injective, bijective and surjective map?
What you continue to fail to demonstrate that EVERY Real numbers can be mapped to unique natural number. What you fail to demonstrate is a bijective map between R and N.
Let me ask you this, how is it possible for a Real to NOT be on the list? My listing method is informational, I go through every option that can exist in a certain information space, and then it moves to a higher information space, and then to an even higher one, and so on, and so on. eventually, any finite piece of data will be on the list at some point. So if it's a number you can describe using information, it means necessarily that it will be on the list, how can it not?
I have demonstrated that every Real can be on the list, but you seem to be incapable of understanding it. I have no idea why
You keep demonstrating that ANY GIVEN real number can be mapped to a natural number... continue to fail to demonstrate that EVERY Real numbers can be mapped to unique natural number
How is that not a contradiction, So if it can list every given number in the Reals, then it lists all the Reals! You are saying it yourself!
Again, tell me how it is even possible for there to be some
finite number (all numbers are) or
representation/function that is not listed at some point, in a list that includes all finite information as list items inside it? Tell me!
So yes, I have shown that EVERY Real number is on my list because I HAVE shown that every possible "language description" is on my list. If every possible
description is listed, it follows that every possible number is on the list as well, because a number is a
description of math! This is so obvious!! How are you missing it? Please don't blame me for your inability to comprehend simplicity!
Just answer me this one simple question, let's assume there is ONE Real number that is not listed. Would you agree that this Real number has a finite representation of some kind?