Re: Peano curve is wrong

In article <b95f2336-afef-44e5-85d7-977e20062bf4@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
qiuzhihong <qiuzhihong@xxxxxxxxx> wrote:
On Apr 6, 9:36=A0am, magi...@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
In article <ft8kem$e0...@xxxxxxxxxxxxxxxxxx>,

Arturo Magidin <magi...@xxxxxxxxxxxxxxxxx> wrote:

I hate it when the right analogy occurs to me a few hours after the
fact...

It's like arguing that the proof that 1+1=3D2
is incorrect because the argument relies on claiming that a+a is
always equal to 2, which is not true. (Indeed, "a+a=3D2 for all a" is
false, but that is not what is used to prove that 1+1=3D2).

Better analogy:

It's like arguing that 16/64 is NOT equal to 1/4, because one cannot
simply cancel the digit 6 from both numerator and denominator to get
the answer. It is indeed correct that one cannot, in a rational number
q, simply cancel digits from numerators and denominators and expect
the result of such action to be another representation of q. But that
does not mean that a proof that uses that 16/64 is equal to 1/4 is
incorrect, just because the argument you put forth (cancelling digits)
is invalid. In fact, one can prove that 16/64 IS equal to 1/4, for
example by noting that the cross products 4*16 and 64*1 are equal. So
just because you can come up with examples where the cancelling of
digits is invalid (e.g., 15/54 is not equal to 1/4), it does not mean
that "16/64 =3D 1/4" is incorrect or that there is a gap in asserting
that equality.

If you think so, save your time.

If I think ->what<- I should save my time? If I think 16/64 is equal
to 1/4?

Or think about this if your logic is not so simple:

What logic?

g(a) =3D lim_{n-->oo} f_n(a).
Even if lim-f_N : {[0, 1] -> (rational pairs in the plane)}*

* means, the limit of f_N finish the mapping between [0, 1] and
rational pairs in the plane,
it's still has all the points in the plane are the limit pionts of
sequence f_N.

I'm sorry, but this is, as far as I can tell, gibberish unconnected to
the points I made in my post. Did you bother to read it, or did you
decide that anything short of praise for your (nonexistent) keen
insight is not worthy of your time or attention?

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

Relevant Pages

  • Re: Peano curve is wrong
    ... Arturo Magidin wrote: ... I hate it when the right analogy occurs to me a few hours after the ... simply cancel digits from numerators and denominators and expect ... incorrect, just because the argument you put forth ...
    (sci.math)
  • Re: Peano curve is wrong
    ... Arturo Magidin wrote: ... I hate it when the right analogy occurs to me a few hours after the ... simply cancel digits from numerators and denominators and expect ... incorrect, just because the argument you put forth ...
    (sci.math)