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

On 9/10/2024 1:33 PM, Moebius wrote:

Am 10.09.2024 um 22:25 schrieb Chris M. Thomasson:

On 9/10/2024 12:31 PM, Moebius wrote:

Am 10.09.2024 um 21:05 schrieb Chris M. Thomasson:

On 9/10/2024 11:42 AM, Chris M. Thomasson wrote:

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?

>
Actually, there

>
is NO
>

unit fractions in that gap[.]

>
:-)
>

>
>
How about:
>
1/1----->(1/4 + 1/4 + 1/4)------>1/2
>
1----->.75----->1/2
>
?
>
There are infinite[ly many] unit fractions in the gap?

 Nope. There is NO unit fraction in te gap (between 1/2 and 1/2).

There is no gap between 1/2 and 1/2. That is zero. You made a typo and meant 1/1 and 1/2 right?

Hint: 1/4 + 1/4 + 1/4 = 3/4 is not a unit fraction. :-)
 How many rounds do you want to... :-)
 

Well, there are infinite unit fractions that can be used for a normalized distance between any two n-ary points in space, right? Well, the two points would need to be different. If they were the same then the length of the gap would be zero.