>>12459982>infinite subset is represented by some description or an algorithm>deeply problematic> it could be that two different descriptions or algorithms can be proved to be equivalent>it is self-referential>infinite choice, not requiring any algorithm or description>there are no examples of such sequenceIt seems like you are entangled in your own shoelaces.
I can write down a symbol of infinitely many things.
Observe, as I describe Natural Numbers with a picture. It comes in a finite amount of bytes, and you can even see the actual number of them near the picture.
But how to give that symbol a meaning? What is a semantic for that picture?
One way I could do that is by recognising Peano construction in this pictorial form.
Other way I could do that is by defining a datatype with accociated mappings.
There are other ways as well.
So then we are inquiring "are those semantics related somehow?"
We associate them with a same symbol, so the relation is evident.
Maybe we can even describe some semantics in terms of the other semantics, and vice versa.
What is the meaning of 2? I can give meaning to that symbol by different symbols, like 1+1, 0+2, 2+0. Somehow they are related.
We can use symbols as meanings for symbols.
What to make of it?
My haskell program with a definition of all natural numbers will compile, and even will produce some result in the finite amount of time.
There it is, in all its glory:
x = [0..] :: [Integer]
Somehow the sequence of instructions for the processor is still finite, and yet there is a symbol for every natural number.
Strange, don't you think? Probably just an elaborate hoax.
