Re: How many different unit fractions are lessorequal than all unit fractions?

Chris M. Thomasson formulated on Tuesday :

On 9/10/2024 4:09 AM, FromTheRafters wrote:

Chris M. Thomasson brought next idea :

On 9/9/2024 11:49 AM, WM wrote:

On 09.09.2024 17:27, Python wrote:

Le 09/09/2024 à 17:15, Prof. Dr. Mückenheim, aka WM a écrit :

On 09.09.2024 16:32, Python wrote:

Le 09/09/2024 à 12:19, Prof. Dr. Mückenheim, aka WM a écrit :

>

1/n is not in (0, x). Sure. So what? Nevertheless there are Aleph_0 unit
fractions in (0, x). No need for 1/n to be there, there far enough other
fractions.
>

If you cannot understand mathematics consider the simplest logic:
If a sequence of different real points exists on the positive real axis, then it has a beginning. Otherwise it could be a cloud but not a sequence.

>
Oh wow. You need help! Or we do for even giving you the time of day. YIKES!!!!!!!!!!

 Actually, I think he is close to correct. The thing is, he wants the first term of the sequence to be last. The reals are not a sequence, but the unit fractions are and they start with 1/1 not at some imagined other end. You need a first and likely a next to start.

>
So, I am thinking there is a unit fraction that fits in the simple gap of 1/1 and 1/2:
>
1/1----->1/4------>1/2
>
?
>
Fair enough? Is this getting on track or going off the rails?

That's not the same ordered sequence, but as an interval and having a measure called distance two of these 1/4 length segments will indeed 'fit' between the one and the one-half endpoints.
Not the same as inserting an element in an out of order sequence.