Second Proof 1=0

[Eodnhoj7]

A) 1 --> (1,1)=2 ---> (1,1,1)=3 ---> (1,1,1,1)=4 ---> (.....) ----> (1n ---> infinity)
***this can be observed as a standard 1 dimensional number line.

B) (1 <---> 1) <---> ((1--->1)&(1<---1))

C) (1--->1) <---> ((1--->2)--->3)...)

D) (1--->1) = (1n ---> infinity)

E) (1n ---> infinity) = (1--->1)◇
****"◇" means change or changing...wrong symbol but will do for now.

F) ((1--->1)&(1--->1)) contains as an element (1--->1)◇ therefore ((1--->1)&(1--->1))◇

G) (1<--->1) <----> ((1--->1)&(1<---1))◇ therefore ((1n ---> infinity) ---> 1)

H) ((1--->(1n--->infinity))&((1n--->infinity)--->1)

J) 1 <---> (1n ---> infinity)

K) 1 = 1◇

L) 1◇ <---> (1--->1)

M) (1--->1) ---> (1--->0) because 1---> (1n-->infinity)=
***1 approaching infinity always requires one manifesting fractions (or fractals on the number line) thus 1 approach to requires 1.1, 1.2, 1.3, etc. As 1.11, 1.12, 1.13, etc.

N) 1◇ <---> ((1--->1) & (1--->0))

O) 1◇ <---> (1 & 0)

P) 1◇ = (1 & 0)

Q) 1 = 1◇ therefore 1 = 0

[Eodnhoj7]

a) 0
b) 0 ---> 0
c) 0 <--- 0
d) 0=0
e) (0=0)
f) 1(0=0)
g) 1(=)
f) 1(=)1
h) (1(=)1)
i) 0(1(=)1)
j) (0(=)0)
k) (1(=)0)

[Skepdick]

b) 0 ---> 0
c) 0 <--- 0

What do the functions ---> and <--- mean?

If you use LISP you can trivially invent your notation and define them as whatever you want.

https://repl.it/repls/AlienatedTurbulentAnimatronics

[Eodnhoj7]

b) 0 ---> 0
c) 0 <--- 0

What do the functions ---> and <--- mean?

If you use LISP you can trivially invent your notation and define them as whatever you want.

https://repl.it/repls/AlienatedTurbulentAnimatronics

Or I can explain it in english and you can type it in....

Some symbols have to be taken intutively, and geometric forms seem to tap best into this considering they are pure assumptions. We assume forms. We assume through forms. Space is the language of reality and is reality.

So to end the boring preaching and try to find some common ground...we are left with a language game...again...take the following for what you can "assume":


("tends toward", "directed to", "asserts", "proposes", "projects", "if then", "defines", "1" as static form, "1" as progressive dynamic change,...) ---> (x)

[Skepdick]

Or I can explain it in english and you can type it in....

Some symbols have to be taken intutively, and geometric forms seem to tap best into this considering they are pure assumptions. We assume forms. We assume through forms. Space is the language of reality and is reality.

So to end the boring preaching and try to find some common ground...we are left with a language game...again...take the following for what you can "assume":


("tends toward", "directed to", "asserts", "proposes", "projects", "if then", "defines", "1" as static form, "1"

Even in English, none of these permutations make sense.

0 tends toward 0
0 directed to 0
0 asserts 0
0 proposes 0
0 projects 0
0 if then 0
0 defines 0

[surreptitious57]

Only the last one [ 0 defines 0 ] makes any real sense because it is a tautology but the others are not sufficiently rigorous
Non mathematical language is more ambiguous and less precise than mathematical notation which is why it is never used
The best expression to define the relationship is the most obvious one 0 = 0 [ also a tautology but all true equations are ]

[Eodnhoj7]

Or I can explain it in english and you can type it in....

Some symbols have to be taken intutively, and geometric forms seem to tap best into this considering they are pure assumptions. We assume forms. We assume through forms. Space is the language of reality and is reality.

So to end the boring preaching and try to find some common ground...we are left with a language game...again...take the following for what you can "assume":


("tends toward", "directed to", "asserts", "proposes", "projects", "if then", "defines", "1" as static form, "1"

Even in English, none of these permutations make sense.

0 tends toward 0
0 directed to 0
0 asserts 0
0 proposes 0
0 projects 0
0 if then 0
0 defines 0

the equal sign is a symbol and hence a context.

the same occurs for its replication to other context, through equivocation:

"equal" regresses to

tends toward
directed to
asserts
proposes
projects
if then
defines

thus "equality" as a context of definition in both symbol and word is subject to "equivocation" and observes an inherent recursion of context

To have (0=0) be the same as (=) is unconventional but no contradiction.

(1(0=0)1) where zero effectively is "nothing" can be taken as a stance equal to (1(=)1)

Or you can observe:

(1(=)1) & (0(=)0) therefore (1(=)0) because of (=) acts as a connector that is a common variable between the two.

Is it unconventional? Yes. Is "context" a contradiction when each symbol and set of symbols is a "context"...no.






The first "f" step observes ( ) as a set. It is "1" set just like (2) is one set of 1's or 3 is one set of 1's (and 2 and 1 respectively but 2 is a set as well).

The identity of all numbers, as sets of one, are identifiable by one. If I count 3 oranges, while there may be distinct oranges, it is still one set of the same fruit. So every countable object, even 4 cars, is still a variation of the one thing.

So 2 oranges plus 3 oranges is one set of five oranges...1 orange through 5 variations....one and many, but we assume this one intuitively as for practical manners we use 5. Even if we count 5 different objects, we still count them as variations of "object" which is one set.

This sets up for step "g"...0 is an empty value. Void of anything. Equality, as the direction of one zero to another (observed in steps b and c) sets the foundation for what the identity property as a context is...thus when observed the context of 1(0=0), as one context, we are observed one reciprocal loop.

Equality is the grounding of any mathematical or logical proposition, with "proposition" rooted in the Latin "propositio" meaning "to set forth", which inherently is a "loop" due to its directional properties.

This 1(=) which sets the ground for identity, observes 1 (loop).

This loop, beginning with the negation of the two 0's through the equality sign (as equality represents a loop, but because of 0=0 meaning "nothing" it is the canceling of 0 into a loop), inturn as one empty set "loops" itself into a new set of (1(=)1).

Now this set of 1 equals 1 will of course be 1 set, however it will also be 0(1(=)1) considering 1 looping itself is fundamentally empty. This is premised under step e (0=0)...so
0(1(0=0)1).

Thus we observe (0(=)0) where before (0=0) was the context, then (=) was it's own context, then both (0(=)0) simultaneously as ((0=0)=(0=0)) looping through voiding itself into further and further empty contexts (which accounts for this continual looping of 1 resulting in 1,2,3,... in the number line).

Thus (=) acts as a link between (1(=)1) and (0(=)0), there (=) acts as a transitive property connecting 1 and 0.

[Eodnhoj7]

Only the last one [ 0 defines 0 ] makes any real sense because it is a tautology but the others are not sufficiently rigorous
Non mathematical language is more ambiguous and less precise than mathematical notation which is why it is never used
The best expression to define the relationship is the most obvious one 0 = 0 [ also a tautology but all true equations are ]

Rigourousness is assumed, and thus is grounded in an inherent esthetic quality to certain degrees...ie the observation of beauty through an inherent symmetry of parts (or absence in some cases with post modern arts).

Mathemetical language, is subject to the context in which it is observed and has ambiguity in many respects:

+1 and +1 can have various meanings dependent upon the context: +1 as a positive number on a number line or +1 as addition within an equation. The symbols are thus defined within the context of there interpretation.

To observe 0=0 effectively observes 1 context as 1(0=0), where 0 effectively is canceled by its own nature and we are left with 1(=) where equality is a context inseparable from 1. You cannot seperate mathematical operators from the numbers as they are interwined contexts.

To observe (1(=)1) is to observe (1(0=0)1) and furthermore (0(=)0) as recursive contexts within contexts as it continually progresses.

Thus (=) as a context, which exists through (1(=)1) and (0(=)0) observes (1(=)0) where (=) acts as a variable that links the two.

"Equality" is a symbol and definition which fundamentally means nothing and everything. It is expressed through a variety of symbols as a connector thus is "imaginary" in nature.

[Skepdick]

I think this is the book you are looking for: https://www.math.upenn.edu/~wilf/AeqB.html

[Eodnhoj7]

I think this is the book you are looking for: https://www.math.upenn.edu/~wilf/AeqB.html

viewtopic.php?f=26&t=27365

Still stuck with a language game...the simpler the language the more options.

[Skepdick]

Still stuck with a language game...the simpler the language the more options.

A language is worthless without its interpretation rules.

You could argue that 'dot' is a valid language, but it's only syntactically valid. It has no semantic.

[Eodnhoj7]

Still stuck with a language game...the simpler the language the more options.

A language is worthless without its interpretation rules.

You could argue that 'dot' is a valid language, but it's only syntactically valid. It has no semantic.

Its interpretions rules are expressed through language and thus are assumed and we are left with a metaloop. Thus any rules of interpretation must be inherently assumed and as assumed we are left with the progression of contexts to further contexts with each context (as an inherent loop) inverting to another context.

The dot, as purely assumed for any and everything, shows an intrinsic nature to logic where an inherent form is always present but due to an innumberable degree of assumption it is unprogrammable. Logic, at its root, is not subject to programming as its assumed nature makes it intrinsically empty, where logic becomes nothing but empty contexts.

You want value and meaning, but this lies in "form"; thus unless you program recursive and isomorphic spatial axioms (which is impossible from a finiteness perspective as space is infinite and the phenomenon we "count" are grounded in a spatial nature) you are left with man not being subject to the nature of computation nor "computing" being the "be all and end all of inherent being" but rather a repeated form of it.

All logics cannot be reduced to computation as certain logics, underlying all logics, require a pure inherent assumption that leaves them effectively groundless and foundationless where "void" is the paradoxical foundation....the "assumptive logic" thread observes this as the assumptions that validate all foundations are subject to strict spatial axioms that exist in infinite variations they are directed through eachother.

Logic cannot be programmed nor understood the closer one gets to its "roots"...and its "roots" are inherently empty contexts.

[Skepdick]

Its interpretions rules are expressed through language and thus are assumed and we are left with a metaloop.

No. https://en.wikipedia.org/wiki/Homoiconicity

A language is homoiconic if a program written in it can be manipulated as data using the language, and thus the program's internal representation can be inferred just by reading the program itself.

https://en.wikipedia.org/wiki/Self-hosting_(compilers)

Thus any rules of interpretation must be inherently assumed and as assumed we are left with the progression of contexts to further contexts with each context (as an inherent loop) inverting to another context.

No. https://en.wikipedia.org/wiki/Context-free_grammar

All logics cannot be reduced to computation as certain logics, underlying all logics, require a pure inherent assumption

Yes they can. If you are manipulating symbols on paper, and if you can teach your manipulation rules to a computer - it can be reduced to computation.

If it's a Formal system it's in the Chomsky hierarch.

[Eodnhoj7]

Its interpretions rules are expressed through language and thus are assumed and we are left with a metaloop.

No. https://en.wikipedia.org/wiki/Homoiconicity

A language is homoiconic if a program written in it can be manipulated as data using the language, and thus the program's internal representation can be inferred just by reading the program itself.

https://en.wikipedia.org/wiki/Self-hosting_(compilers)

Thus any rules of interpretation must be inherently assumed and as assumed we are left with the progression of contexts to further contexts with each context (as an inherent loop) inverting to another context.

No. https://en.wikipedia.org/wiki/Context-free_grammar

All logics cannot be reduced to computation as certain logics, underlying all logics, require a pure inherent assumption

Yes they can. If you are manipulating symbols on paper, and if you can teach your manipulation rules to a computer - it can be reduced to computation.

Actually the assumptions cannot be reduced to anything besides "forms" at there most basic level and the computer's basic input output operation is strictly a linear/cyclic form....even this is an "assumption" hence it is its own foundation that follow the same form and function of this "system".

You can have a logical base observing the nature of assumption, which proves that not only are not all logics computable (as this logic observes the nature of the very assumptions which form logic) but computation is subject to underlying "pre-logics".

Strict contextualization is not programmable as it is intrinsically random yet defined through its repetitive nature.

[Skepdick]

Actually the assumptions cannot be reduced to anything besides "forms" at there most basic level and the computer's basic input output operation is strictly a linear/cyclic form....even this is an "assumption" hence it is its own foundation that follow the same form and function of this "system".

This argument happened 100 years ago in Mathematics between the Platonists, Formalists and Intuitionists.

I am not really sure if anybody won or lost that argument. In the end you can interpret it whichever way you want because in the end Mathematics is just syntax. Semantics comes from interpretation.

My bias is Intuitionism. As I would say that a Formalist is a closet Intuitionist, so a Formalist would say I am a closet Formalist too.

If we can agree on each others' propositions - who cares?