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... all the way to the part where he said he got the "Googlephonic stereo ... the highest number of speakers before infinity."
That was a "Googolphonic stereo" - IIRC, It has (10 raised to the one-hundredth power) speakers. Steve missed the fact that a googolplex is one googol raised to the googol power, too. So, one googol is not the highest named number before infinity - but it was a good joke on the Quadrophonic stereos of the time...
So now, ya know where Larry and Sergey got the names. :)
Jim
Googolphonic stereo
I had to spell it "Google" ... c'mon!
Jim
The first number larger than infinity is Aleph
which equals infinity plus 1.
I always thought my Abstract Alegebra professor
was smoking to much dope, but checking on the
web, yes Aleph is for real.
So buzz lightyear could have shorten his phrase of to infinity and beyond to simply 'to Aleph' :)
The first number larger than infinity is Aleph
which equals infinity plus 1.
The standard, plain-vanilla infinity we all know and love is "Aleph-naught" - Propperly written as a Hebrew symbol with a subscript of zero. I'm not at all sure how to do that here. Successively larger infinities can be obtained by exponentiation, but I can't remember exactly how the exponentiation is done off the top of my head, and can't seem to find it in any of my books. "Infinity plus one" is a null concept, though. If you insist, it equals infinity. *Not* Aleph-one.
To make it a little more comprehensible, there are at least two "sizes" of infinity we're all more-or-less used to dealing with. The smaller of the two is the size of the set of all integers. It's also the size of the set of all positive integers, or all points on the Cartesian plane with integer coordinates. This is "Aleph-naught". There are a number of relatively easy ways to prove this to yourself by establishing a bijection between any two of those sets.
There are more "real" numbers between zero and one than there are integers. Infinitely more. You could map all the positive integers (remember, there are just as many of those as there are integers, so this convenience is legitimate) onto real numbers between zero and one with a relatively simple map of f(n)=1/n. Every positive integer is thereby mapped onto exactly one real number between zero and one, and every real number between zero and one is mapped to *at* *most* one positive integer. In fact, the vast majority of the numbers between zero and one still remain un-mapped. In between any two of the real numbers that are mapped, you could re-create essentially the same mapping, and still leave more holes in the map than mapped points. The size of the set of real numbers between zero and one is fundamentally larger than the size of the set of all integers, even though both are infinite. That's "Aleph-one" (Again, propperly a Hebrew character with a subscript of one.)
If I recall correctly, the conjecture that there may be infinite cardinalities in between the Aleph family is called the "continuum hypothesis", and it has been proven that either the continuum hypothesis or its negation could be assumed as an additional axiom of mathematics without affecting anything established in current mathematical systems. (This also means it can't be proven or disproven.)
<edit>fixed a typo. Probably left several others ;)</edit>
lawman
BTW, you left out the other Infiniti
You caught me out, Lawman. I have no idea how to calculate the cardinality of an Infiniti ;)
anyway, anyone got some answers: 1/1 = 1; 1/0 = undefined; 0/0 =?; 0/1 =?.
peace.
I believe 0/0 falls under the undifined category.
I belive that infinity/0 falls under the undefined category. However, if somebody wanted to argue that 1/0 and infinity/0 equals infinity then I wouldn't put up much of a fight as that is how I treat them.
(edited typo - typed 1 instead of 0)
[galactic-guide.com...]
7 Speakers, for TWO ears?
Another anomaly...
Quadrophonic headphones... one pair over your ears, one positioned to the forehead and one to the back of the head?
Guess I am an old fashioned "Stereo is good enough" dude.
