Re: Simple enough for every reader?

On 2025-06-18 13:48:13 +0000, WM said:

On 18.06.2025 11:39, Mikko wrote:

On 2025-06-17 10:57:01 +0000, WM said:
 

On 17.06.2025 12:16, Mikko wrote:

On 2025-06-16 10:50:58 +0000, WM said:
 The error above is that the expression "the last one" is used without
proving that there is a last one.

 If all natnumbers are subtracted, none remains.

 True.
 

If all natnumbers are subtracted in their order, one after the other, none remains.

 The order does not matter,

 But the order exists for all defined natural numbers. We know of each one its predecessor and its successor, if those are existing.

It is also possible to order them differently. Removing all leaves
nothing, whther you remove in some order or another or all at the
same time.

the result is the same anyway.

 That means that none remains. I case of known order we know the last one subtracted.

 But that does not prove that your "the last one" denotes anything.

 How can an ordered set be completely subtracted in its given order without a last one?

Euclid did not specify how to draw a circle. He merely postulated that
for any given centre and radius it can be done. Likewise a set theory
does not specify how one set can subtracted from another. It merely
postulates that it can be done.
--
Mikko