No I rather think that Nelson is a mathematician or a theoretical
computer scientist. NP is one of the most important classes of
computational problems, the problems that can be solved in
non-deterministic polynomial time, and the hebrew letter aleph
is used to denote cardinality of infinte sets: Aleph_0 is the
cardinality of countable infinite sets like the integers and
the rationals, Aleph_1 is the cardinality of the reals and then
there is an infinite sequence of more and more infinite infinities.
computer scientist. NP is one of the most important classes of
computational problems, the problems that can be solved in
non-deterministic polynomial time, and the hebrew letter aleph
is used to denote cardinality of infinte sets: Aleph_0 is the
cardinality of countable infinite sets like the integers and
the rationals, Aleph_1 is the cardinality of the reals and then
there is an infinite sequence of more and more infinite infinities.
aleph null
Aleph-null is the cardinal number of the set of Integers.
(There are as many positive integers as there are both positive and negative integers, and that is Aleph-null. Aleph-null plus aleph-null equals aleph-null.)
http://www.bsu.edu/web/jcflowers1/rlo/mathnumbers.htm
Aleph-null is the cardinal number of the set of Integers.
(There are as many positive integers as there are both positive and negative integers, and that is Aleph-null. Aleph-null plus aleph-null equals aleph-null.)
http://www.bsu.edu/web/jcflowers1/rlo/mathnumbers.htm
vdi_nenna said:aleph null
0 with a / through it.
You're probably right. It's a long time since I took discrete math.
So, change to Aleph_1 and Aleph_2, in my previous posting.
Christer said:No I rather think that Nelson is a mathematician or a theoretical
computer scientist. NP is one of the most important classes of
computational problems, the problems that can be solved in
non-deterministic polynomial time, and the hebrew letter aleph
is used to denote cardinality of infinte sets: Aleph_0 is the
cardinality of countable infinite sets like the integers and
the rationals, Aleph_1 is the cardinality of the reals and then
there is an infinite sequence of more and more infinite infinities.
After hanging around here a while, I now think of NP as initials for
Mr. Pass as opposed to the complexity class.
BTW, the cardinality of the reals is often denoted 'c' (continuum).
The conjecture that c=Aleph_1 actually turned out to be one
of the strangest problems in mathematical logic. (This is
the so-called 'continuum hypothesis'.) Whether this
is true of false (and here's the fun part) turned out to
depend on whether you work in a logic system
which includes something called the Axiom of Choice.
Dennis
i have just done search in goggle and
http://www.moonromance.net/storyview.php?storyid=7193
check this one out
http://www.moonromance.net/storyview.php?storyid=7193
check this one out
Continuum Hypothesis and Axiom of Choice
Actually, the continuum hypothesis, ie the statement that there is no infinite set larger than the integers and smaller than the real numbers, doesn't depend accepting or rejecting the axiom of choice, but is independent. It makes for some interesting reading.
http://www.ii.com/math/ch/
Actually, the continuum hypothesis, ie the statement that there is no infinite set larger than the integers and smaller than the real numbers, doesn't depend accepting or rejecting the axiom of choice, but is independent. It makes for some interesting reading.
http://www.ii.com/math/ch/
Re: Continuum Hypothesis and Axiom of Choice
You are right of course; it's been way too long since
I'd studied this stuff.
Dennis
mirlo said:Actually, the continuum hypothesis, ie the statement that there is no infinite set larger than the integers and smaller than the real numbers, doesn't depend accepting or rejecting the axiom of choice, but is independent. It makes for some interesting reading.
http://www.ii.com/math/ch/
You are right of course; it's been way too long since
I'd studied this stuff.
Dennis
Yes, Aleph is the first letter of the Hebrew alphabet.
It has the meaning of ox and in tarot it corresponds to
The Fool. It corresponds to the primal energy, spirit and
to the element of air. It also indicates limitless possibilities.
And many other things besides. An ox is a motive force.
It has the meaning of ox and in tarot it corresponds to
The Fool. It corresponds to the primal energy, spirit and
to the element of air. It also indicates limitless possibilities.
And many other things besides. An ox is a motive force.
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