I've been thinking about something related recently.
I was wondering if the only number that truly exists is One. Zero is nothing and therefore doesn't exist, and all that does exist is eventual composed of One.
I was wondering if the only number that truly exists is One. Zero is nothing and therefore doesn't exist, and all that does exist is eventual composed of One.
https://www.youtube.com/watch?v=mPn2AdMH7UQ (15m video starring Don Knuth) https://www.youtube.com/watch?v=1eAmxgINXrE (1h15m video starring John Conway)
It may be the case that you've already heard of the Surreal Numbers, but I remain confident you enjoyed learning about them. :)
In my book, something like two or ten exists - because my kid can hold up 2 fingers and say 2 or all of them and say 10. I am saying that you can actually count to those numbers in physical space.
But at some point, the number is like larger than the number of atoms in the universe (or whatever you think is the biggest domain we can count) and once you go past that number, your counts represent abstract numbers that don't have a physical representation.
This despite there being ( 10 x 9 ) groupings of pairs of those 10 marbles?
For any of those 90 pairs we can show a physical example of ( this marble, that marble ).
In my comment I said "or whatever is the largest domain you think you can count". So in your example we still run out of physical stuff that can be counted (at 90) right?
> So in your example .. right?
Not at all, and it's pretty clear why :)
They spend some 350 pages proving 1 + 1 = 2 from very primitive principles, including the existence of numbers themselves. Turns out, numbers, even One, are non-primitive constructs.
We only share our object reality not our sense of Being and so while for me this seems like a singular concept I can not witness what it is for you or anyone else.
The duality of existence and non-existence means that We all share fundamentals, totally agree with you there.
Do you mean zero implies one by its lack of absence?
I'm wondering that if we were to consider a platonic view of forms through planes of physicality, idea and thought is it the case that all that exists across them is One?