# Boost :

Subject: Re: [boost] New Boost.XInt Library, request preliminary review
From: Gottlob Frege (gottlobfrege_at_[hidden])
Date: 2010-04-02 02:48:27

I've mostly missed the train on this, but if I could quickly bring up

1. infinity is not a number
2. something about 1/inf and infinity stuff being INEXACT

my responses:

2. 1/inf = 0 *IS* exact. It is inexact while approaching inf, but
finally exactly 0 'at' infinity.

1. depends on your definition of 'number'. You can definitely say
infinity is not an integer. (NaI ?) But for a reasonable definition
of 'number' infinity IS a number (or more accurately, a bunch of
numbers, as there is a bunch of infinities).

The best definition, that I know of for number is "The answer to the
question: 'how many?' " and infinity fulfills that definition.

And now some background, and why I bring this up - Many moons ago when
the web was young-ish, I took Gottlob Frege as a 'web-identity' (back
when alta-vista was a search engine and Yahoo was king and wanted all
your personal info, etc...), and as a habit I have carried it around
ever since. Call me Gottlob on the web vs Tony (my real name) and I
usually don't even notice.

Anyhow, the real Gottlob Frege was a turn of the century
Mathematician/Philosopher. He wrote an excellent book called "The
Foundations of Arithmetic" - one of my favorites. It mainly attempted
to answer the question "what is a number". The first answer is that
it is the answer to the question 'how many' (for mathematicians this
is now called 'cardinality'). After that answer the book moves
forward and gets quite interesting and complicated.

Anyhow, whenever anyone says infinity is not a number, I feel
compelled to reply that it answers the question 'how many", and thus
is a number. ( Typically the more precise question is 'how many
integers are there" and the answer being aleph0 or 'aleph-not' - the
first infinity).

Anyhow, feel free to ignore this. I'm not actually taking sides on
whether/how you treat NaN/infinity - sounds like you may be able to
avoid it altogether.

P.S. for the logicians out there - he was also basically the first to
introduce rules for quantifiers "For all", "there exists at least
one", etc;
And for all those wearing programmer-hats instead of their mathematician-hats:
I also consider Gottlob Frege the father of 'duck-typing'.
A man before his time...

Tony