Re: Contradiction or paradox

On May 19, 4:24 pm, "Jesse F. Hughes" <j...@xxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
See, I repeat, you have not shown that subtraction satisfies the
hypotheses.

What hypotheses? You have given no hypotheses.

You pathetic liar.

self-applied

Right here is the theorem we have been discussing:
http://us.metamath.org/mpegif/ecoprass.html

Here is the top of that page. Apologies for typographic oddities
resulting from cut-n-paste.

Description: Lemma used to transfer an associative law via an
equivalence relation.

Hypotheses
------------
ecoprass.1|- D = ((S X. S)/.R)

ecoprass.2|- (((x e. S /\ y e. S) /\ (z e. S /\ w e. S)) ->
([<.x, y>.]RF[<.z, w>.]R) = [<.G, H>.]R)
ecoprass.3|- (((z e. S /\ w e. S) /\ (v e. S /\ u e. S)) ->
([<.z, w>.]RF[<.v, u>.]R) = [<.N, Q>.]R)
ecoprass.4|- (((G e. S /\ H e. S) /\ (v e. S /\ u e. S)) ->
([<.G, H>.]RF[<.v, u>.]R) = [<.J, K>.]R)
ecoprass.5|- (((x e. S /\ y e. S) /\ (N e. S /\ Q e. S)) ->
([<.x, y>.]RF[<.N, Q>.]R) = [<.L, M>.]R)
ecoprass.6|- (((x e. S /\ y e. S) /\ (z e. S /\ w e. S)) ->
(G e. S /\ H e. S))
ecoprass.7|- (((z e. S /\ w e. S) /\ (v e. S /\ u e. S)) ->
(N e. S /\ Q e. S))
ecoprass.8|- J = L
ecoprass.9|- K = M

Assertion
-----------

ecoprass|- ((A e. D /\ B e. D /\ C e. D) -> ((AFB)FC) = (AF(BFC)))

The formulas ecoprass.1-9 are clearly listed as hypotheses which must
be verified before the conclusion is justified. And this is exactly
how the theorem is later applied to addition:

Thanks. How is that later justified, as you say? What I posted ages
ago did not show any checks when the substitution is made.

I see statements about all of mathematics coming from a small number
of axioms - ZF, some logic, Peano's Axioms - but in the proofs I see
hundreds of axioms, rules, definitions. I also wonder why simple
proofs take hundreds of lines. Can't we prove 2+2=4 in a few steps (2
is 0'' and 4 is 0'''' etc.)?

1. Where did the lines in the proofs come from - what creates them?

2. What assures that they follow some specific syntax? What if they
don't follow the correct syntax?

3. Can the general public use the system to create proofs
automatically? If yes, then how, and if no, then why not?

4. What is creating the massively long expressions that occur? How do
we know that they are correct? How do we know that they are
meaningful?

5. When did he most recently add a new axiom, rule, definition etc. to
the system? What is the source of the complete sets of axioms, rules,
definitions etc.? Do you have to keep adding to the system to prove
all statements of arithmetic such as 2+(3*5)=17?

C-B

First, check that
addition satisfies the hypotheses and then conclude that it satisfies
the conclusion.

You have never shown that subtraction satisfies these nine hypotheses.

--
Mo memorized the dictionary
But just can't seem to find a job
Or anyone who wants to marry "Memorizin' Mo",
Someone who memorized the dictionary. Shel Silverstein


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