Re: 2N=E

Am 07.11.2024 um 23:29 schrieb Chris M. Thomasson:

On 11/7/2024 1:34 PM, Moebius wrote:

Am 07.11.2024 um 22:08 schrieb Chris M. Thomasson:

On 11/6/2024 4:07 PM, Moebius wrote:

Am 06.11.2024 um 22:04 schrieb Chris M. Thomasson:
>

sum [series],
>
1+2+3+4+5+6+...

>
is not a natural number. :-P

>
Since there is no largest natural number, the sum is a natural number?

>
Nope. There simply is no "sum".

I mean: there is no sum of _all_ the terms: 1, 2, 3, ...

The [partial] sum keeps getting bigger and bigger

Sure. But there is no sum of ALL natural numbers (i.e. n in IN).

However, each iteration is a sum and is a natural number?

Sure. Hint:
 >>>> For all n e IN:
 >>>>
 >>>>         1 + ... + n
 >>>>
 >>>> is a natural number (i.e. in IN).
(Simple proof by induction.)
Nuff said.