Re: Logarithm of transfinite numbers

In <1142285659.034470.243360@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
03/13/2006
at 01:34 PM, matt271829-news@xxxxxxxxxxx said:

Just because the usual definitions and methods for finite numbers
appear to fail does not necessarily mean that the concept cannot be
naturally extended.

As has been pointed out before, the "usual definitions and methods for
finite numbers" fail for integers; logarithms of integers are not, in
general, integers. So if you want to define logarithms of arbitrary
cardinals or of arbitrary ordinals, you'd better plan on them being
something other than cardinals or ordinals.

It may be that the logarithm has a natural and
compelling extension to transfinite numbers,

But until you demonstrate that you understand the issues, nobody is
going to take the suggestion serious; there have been too many cranks
suggesting too many nonsensical ideas, and the well has been poisoned.

It would need someone smarter than me to figure it out though,

But what they figure out may be that your suggestion, as stated, makes
no sense. If you aren't volunteering, but rather want someone else to
pursue your suggestion, then it is incumbent on you to formulate it
coherently and to explain why it is a reasonable investment of their
time.

--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>

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