Sujet : Re: How many different unit fractions are lessorequal than all unit fractions?
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 07. Oct 2024, 19:05:49
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <1a925120-7637-4eac-87bf-749f1befe54f@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
User-Agent : Mozilla Thunderbird
On 10/5/2024 3:33 PM, WM wrote:
On 05.10.2024 20:12, Jim Burns wrote:
On 10/5/2024 5:43 AM, WM wrote:
[In] many cases it is correct.
>
"Many cases" is insufficient when
the argument requires "all cases".
>
My argument requires only one case,
Your argument,
in order to _be an argument_
needs to _show_ its result is true.
A widely.used way to _show_ a result is true
is to assemble mini.argument.forms,
each of which _must_ end not.first.falsely.
⎛ For finite beings,
⎝ no first false requires no false.
A mini.argument.form which
_must_ end not.first.falsely
ends not.first.falsely _in all cases_
The mini.argument.forms
⎛ ∃x∈X: ∀y∈Y: x⫷y
⎝ ∀y∈Y: ∃x∈X: x⫷y
and
⎛ ∀y∈Y: ∃x∈X: x⫷y
⎝ ∃x∈X: ∀y∈Y: x⫷y
are distinguished by, firstly,
ending not.first.falsely in all cases,
and, secondly,
NOT ending not.first.falsely in all cases.
The first shows may show us something.
The second, not so much.
My argument requires only one case,
The argument you present has nothing beyond
demanding your preference _be_ true,
an argument which is not.even.wrong.
In what may be an excess of charity,
I propose that you've made an _error_
which would make you _wrong_
which would be an improvement over not.even.wrong.
In order to improve to _wrong_
your (hypothetical new) argument requires
mini.argument.forms which end not.first.falsely
in all cases.
My argument requires only one case,
best demonstrated with endsegments E(n).
The intersection of all *infinite* endsegments
is infinite, because
they all contain the same natural numbers which
have not yet been eliminated by
the process E(n+1) = E(n) \ {n}.
The intersection of all end.segments is
the set of natural numbers in each end.segment.
Each natural number is not.in one or more end.segment.
That creates a problem (but for only you).
Your attempt to fix the problem involves
a change of the definition of intersection, or
of natural number, or of something else.
Changing what you think "infinite" means
from what we mean by "very large finite"
to what we mean by "infinite"
would fix all that,
but that includes you being wrong,
and you prefer being not.even.wrong.