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Finlayson's slate
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Ross A. Finlayson
Dec 20, 2018, 10:08:00 AM12/20/18
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> Cantor's nested intervals theorem <-> Finlayson's EF as counterexample
> Cantor's antidiagonal argument <-> Finlayson's EF as counterexample
> continued fractions <-> Finlayson's EF as counterexample
> Cantor's indicator function theorem <-> Finlayson's symmetrical
> mapping as counterexample
> Zuhair's binary tree theorem <-> Finlayson's BT = EF as counterexample
> Cantor's powerset theorem <-> Finlayson's powerset as order type as
> successor construction, and a dialetheic ur-element
> Russell's negated correlates <-> Finlayson's note on statement of
> structurally true languages
> irrationals uncountable <-> Finlayson's "A function surjects the
> rationals onto the irrationals"
> Cantor's antidiagonal argument <-> Finlayson's EF as counterexample
> continued fractions <-> Finlayson's EF as counterexample
> Cantor's indicator function theorem <-> Finlayson's symmetrical
> mapping as counterexample
> Zuhair's binary tree theorem <-> Finlayson's BT = EF as counterexample
> Cantor's powerset theorem <-> Finlayson's powerset as order type as
> successor construction, and a dialetheic ur-element
> Russell's negated correlates <-> Finlayson's note on statement of
> structurally true languages
> irrationals uncountable <-> Finlayson's "A function surjects the
> rationals onto the irrationals"
Ross A. Finlayson
Dec 27, 2018, 3:09:20 AM12/27/18
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I keep all that.
j4n bur53
Dec 27, 2018, 5:33:04 AM12/27/18
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> 1+1=2 <-> Finlayson's herpes 1+1=3
Jew Lover
Dec 27, 2018, 10:32:01 AM12/27/18
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Ross A. Finlayson
Dec 28, 2018, 1:14:54 PM12/28/18
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Ross A. Finlayson
Dec 30, 2018, 2:12:39 PM12/30/18
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is a similar way, there's only one
function not establishing structure
outside the space that
it has the values. "
Infinitesimals:
Cantor, cholera (bacteria)
Burse, amoebae (parasite)
Finlayson, herpes (virus)
Cantor can't have cholera,
for Burse it's a parasite,
I think I have all the viruses.
Or, "virii".
The action or motion of
drawing the points of the
line, whether this is always
under a constant function of
time, or what, establishing the
continuous domain, it is a simple
result that line-drawing sweeps
the line while no Cartesian Cantorian
functions admit any such function,
of course with the complete ordered
field as the equivalence classes of
sequences (or, series) that are Cauchy.
Whether as a constant function of time
in t[0,1] or not, it also so basically establishes
such a thing for example with Peano's
"constant infinitesimals" (cholera).
Line-drawing: now in remedial.
1.0: usually "measure theory".
I can write measure theory in that.
Ross A. Finlayson
Dec 30, 2018, 2:35:09 PM12/30/18
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here for example I do so, briefly:
https://groups.google.com/d/msg/sci.math/osVMgEVoxFg/vgjZ30CKAwAJ
f(n), n e N = dom(f)
n/d, n -> d, d -> oo
n > m => f(n) > f(m), monotone strictly increasing
f(n+1) - f(n) = f(m+1) - f(m), constant monotone
extent:
0 = 0/d e ran(f)
1 = d/d e ran(f)
density:
for each x in [0,1], there's a ran(f) in all neighborhoods of x
...
completeness:
the least-upper-bound for finite subsets of ran(f) is in ran(f)
the least-upper-bound for infinite subsets of ran(f) = 1 and is in ran(f)
measure:
measurable subsets {0, ..., f(n)} for n-set {0, ..., n}, or,
measurable subsets {f(m), ..., f(n)} for n > m form a sigma-algebra
Ross A. Finlayson
Aug 4, 2019, 9:00:28 PM8/4/19
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