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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Wed, 30 Oct 2024 11:43:26 -0400
Organization: Peripheral Visions
Lines: 15
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References: <vb4rde$22fb4$2@solani.org>   <d316baa3-de5b-4644-86ff-beacad9df107@att.net> <vfd97u$2jtos$1@dont-email.me> <276fc9df-619b-4a10-b414-a04a74aa7378@att.net> <vfe5d5$2olom$1@dont-email.me> <88e6a631-417a-4dd0-9443-a57116dcbd28@att.net> <vfg07k$1chpe$1@solani.org> <7a1e34df-ffee-4d30-ae8c-2af5bcb1d932@att.net> <vfgil3$38pn6$1@dont-email.me> <6a90a2e2-a4fa-4a8d-83e9-2e451fa8dd51@att.net> <vfgqoc$39o4h$2@dont-email.me> <acd4aad3-9447-45a9-bafd-f8b93d781827@att.net> <vfj3v0$1e96h$2@solani.org> <vfjg9h$3rjvp$2@dont-email.me> <vfkqlr$3fii$1@solani.org> <vfl8o7$3mnmt$4@i2pn2.org> <vflfq9$f82l$1@dont-email.me> <vflovl$1fpr2$3@solani.org> <vfm2m5$iasq$1@dont-email.me> <vfnmo3$ui6v$1@dont-email.me> <vfo5rf$1178s$1@dont-email.me> <vfoqqr$14lcc$2@dont-email.me> <vfotg8$15r9a$1@dont-email.me> <0e5fb47d-60f7-42bb-beec-4a9661c807da@tha.de> <vfqbrm$1gqu7$1@dont-email.me> <vft6n5$246cp$5@dont-email.me> <vftago$25nkf$1@dont-email.me> <vftedi$26a4v$1@dont-email.me>
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on 10/30/2024, WM supposed :
> On 30.10.2024 13:57, FromTheRafters wrote:
>> WM explained :
>
>>> NUF(0) = 0, NUF(1) = ℵo. Therefore NUF must grow but cannot grow by more 
>>> than 1 at any point x of the real axis.
>> 
>> The number of unit fractions less than x is always aleph_zero for positive 
>> x.
>
> Believe what you like without foundation.
> If ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 is true, the NUF(x) grows in steps of not more 
> than 1.

Wrong.