Hi Nelson,
Slightly off topic but I was wondering if the name Aleph was coming from the detector in particle physics. Since you have a patent named supersymmetry, it would be a stange coincidence ...
Akira
Slightly off topic but I was wondering if the name Aleph was coming from the detector in particle physics. Since you have a patent named supersymmetry, it would be a stange coincidence ...
Akira
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:
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.
I'm no math wiz. I remember it from some math class and always thought it sounded cool.
Cool name for a band maybe...😉
Cool name for a band maybe...😉
Christer said:
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/
I always thought "the sciences" were just sub-sets of physics, and physics just a sub-set of applied math.
Dad used to tell me, "If ya can't graph it, ya don't understand it!"
Cyclotronguy/ takes comfort in numbers
Dad used to tell me, "If ya can't graph it, ya don't understand it!"
Cyclotronguy/ takes comfort in numbers
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:
You are right of course; it's been way too long since
I'd studied this stuff.
Dennis
I don't know anything about descrete math or advanced physics,
but I can ad to the "origin of Aleph" discussion that Aleph is also the first letter in the Fenician ( the ancient ancestors of the egyptions ) alfabet. And if I remember correctly it meant Ox.
/Chris
but I can ad to the "origin of Aleph" discussion that Aleph is also the first letter in the Fenician ( the ancient ancestors of the egyptions ) alfabet. And if I remember correctly it meant Ox.
/Chris
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.
Nelson was fascinated by the works of Georg Cantor, a mathematician who spent his last years in an asylum contemplating the mathematical meaning of infinite.
Cyclotronguy
Cyclotronguy
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