Re: What is this thing known as "=" ?

Point well taken. However, " = " represents
quantifiable equivalence,
not qualifiable equivalence.

It has nothing to do with "evidence." The symbol
expresses the relation between two sets of terms
that are
equal, transitive and reflexive. And economic
value, BTW,
_is_ quantifiable.


So, what is your definition of "equal". Is it
quantitative, or
qualitative ?

There are different kinds of "equal". Which kind are
you talking about
?

Nonsense. Equivalence, in a mathematical equation,
has only one meaning. I have recited it for you.
Whatever else you want to say about equivalence may
have some personal meaning to you, but it has nothing to
to do with mathematics.


5 is a natural

SQRT(5) is irrational

5 = SQRT(5) * SQRT(5)

Would you then say that there is no distinction
between a natural and
an irrational ?

I wouldn't say anything at all about your question,
because it has no content.

Maybe you could invent a different kind of " = "
which works
qualitatively instead of quantitatively. I'll bet
it
would be
interesting. That wuold probably keep you busy a
while -

I could busy myself with all sorts of things
that aren't mathematics. Your point is?

Tom


Silly man.

The original question centered on teh validity of the
proof of the
uniqueness of the "zero element" on Wikipedia, and
hwo this proof
misuses the " = " sign, in a failed attempt to
demonstrate "qualitative
equivalence" which is absurd.

If that proof were valid, then naturals would be no
different than
irrationals, as explained above.

Proving my third point, that you are clearly trolling
because these
results are obvious.

I was completely serious when I suggested inventing a
qualitative kind
of " = ". Do you lack the intestinal fortitude to
contemplate inventing
such a thing ? Would that entail such a terrible risk
?


Yes. It doesn't take a whole lot of guts or intelligence
to, as Newton put it, "multiply superfluities." The
risk of remaining uninformed is quite great, I would say.

Tom
.

Relevant Pages

  • Re: Provable in T?
    ... equivalence is provable in T. ... familiar with the Sigma-1-completeness of T. ... familiar with the mathematics and you certainly have nothing to teach ... Second incompleteness theorem, not first. ...
    (sci.logic)
  • Re: What is this thing known as "=" ?
    ... not qualifiable equivalence. ... I could busy myself with all sorts of things ... irrationals, as explained above. ... I was completely serious when I suggested inventing a qualitative kind ...
    (sci.math)
  • Re: What is this thing known as "=" ?
    ... Whatever else you want to say about equivalence may ... Proving the uniqueness of a zero element is equivalent to proving the ... wonderful thing to have the freedom in mathematics to reinterpret ...
    (sci.math)
  • Re: Annoying behaviour of the != operator
    ... But as I understand it, Guido decided that being able to sort arbitrary lists is a feature, not a bug. ... Object Equivalence? ... There is only one 'two' - heck, in pure mathematics, there ...
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  • Re: OT: Half open interval [n,n):was:Re: Accelerated C++: [1,rows] Not so fast
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