Bruijn: limits, intellectual dishonesty and mysticism

On 17 Jan, 08:30, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
lwal...@xxxxxxxxx wrote:
OK, I think I see what the confusion is now.

Here tommy1729 is making an assumption which, while admittedly
intuitive, is false in ZFC. The assumption is that the composition of
infinitely many permutations must itself be a permutation. While it
is definitely true that the composition of finitely many permutations
must be a permutation, it's not true if there are infinitely many.

There is a problem with the implied statement
"the composition of infinitely many permutations
need not be a permutation"
namely that the phrase "composition of infinitely many permutations"
be meaningful.

Plonk! Plonk! How can something be true for the composition of finitely
many permutations and not true if there are infinitely many?

Perhaps Bruijn could answer the following question: Let pi
be the permutation (1 2), that is pi(1) = 2, pi(2) = 1 but pi(m) = m
for all other numbers. Let pi_1 = pi, pi_2 = pi etc., i.e., pi_n = pi
for all n.

Waht does Bruijn say that the composition
pi_1 pi_2 pi_3 ....
is? What is its value at 1?

(Infinitely
many IMHO is just a limiting case of finitely many)

There is nothing "humble" about Bruijn's opinion. But this statement
gives an insight into Bruijn's prejudices and intellectual
limitations.
In particular his frequent but unexamined usage of word such as
"limit" and "limiting". Mathematicians take care to define notions
of limit (for sequences, series, nets etc.) Bruijn showers contempt
on such manifestations of intellectual honesty. Indeed while he pays
lip service to finitism, he admits limiting arguments
(as he knows these are essential in mathematics as practised
by physicists), but his notions of limits are mystical and
anti-theoretical. Of course limit is an infinitary concept
so his claimed finitisism is essentially disingenuous.

Especially because I was flabbergasted to learn that in the
universe of infinite permutations the cardinality of them is the one for
the continuum (c) and not Aleph_0. Did I got this right?

Is Bruijn always so resentful when he learns something?

Victor Meldrew
"I don't believe it!"
.

Relevant Pages

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