Re: how to list all of the real numbers

On 12 Aug, 06:47, lwal...@xxxxxxxxx wrote:
On Aug 11, 7:29 pm, Virgil <vir...@xxxxxxxxxxx> wrote:

Most mathematicians will consider systems of infinitesimals possible,
but unless their own work makes such infinitesimals useful, they are not
liable to spend much energy or time on them.

"Crank" #1: Why accept the Axiom of Infinity?
Standard Mathematician: Because it is useful.
"Crank" #2: Why reject infinitesimals?
Standard Mathematician: Because they are not useful.

So far in both this thread and in "An Inconvenient Truth" the
consensus
among standard mathematicians is that the infinite sets are "useful,"
(in response to HdB's claims that the Axiom of Infinity is not useful)
while infinitesimals are not "useful," which is why the former is part
of standard (or classical) analysis while the latter is relegated to
Nonstandard Analysis.

Huh. The reason HdB reject Infinity is not to do with utility. HdB
believes that there are no infinite sets in reality and therefore
there should be none in mathematics.

.

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