I am looking for an english word meaning beyond infinity....

How about "ultrainfinity"?

Our kids use "Infinity plus one"

-K~

I believe the word you need is "transfinite". The theory of
transfinite mathematics was pioneered by Georg Cantor.

http://www.asa3.org/ASA/PSCF/1993/PSCF3-93Hedman.html

Hi tenai,

pinkfreud-ga should post "transfinite" in the answer box. Indeed, it
means precicely this:

transfinite
http://dictionary.reference.com/search?q=transfinite%20
Going beyond the finite.

--Cynthia

Hi again. I did just notice that "beyond the finite" is *only* infinity.

Oh well. I'll try again!

--Cynthia *blush*

transcendental?

You might have to coin your own word.  

How about:  "buzzlightyearism"

Transfinite numbers, as conceived by Georg Cantor, go beyond infinity:

"Cantor established that there was a distinction between infinity
which is countable, and so-called transfinite numbers which are even
bigger and can't be counted."

http://www.dogsbody.org/news/beyond_inf.html

http://www.laweekly.com/ink/03/16/quark-wertheim.php

I know of no scientific term which is more apt in describing this
concept. There may be words which would be more fanciful or more
poetic, of course.

Transfinite is it. 

Perhaps Google Answers' smartest researcher, mathtalk-ga, would like
to confirm this for the questioner and take the prize.

How about "Infinity to the googoleth power?" I know it's not a word,
but it sounds cool (and it has googol in it from which google is
derived :)

This author suggests "transinfinite" :

http://www.maxpages.com/markphilosophy/Philosophy

and a google search of the term "transinfinite" produces a finite, yet
non-zero set of pages that use the word.

Less popular terms are "hyperinfinite", "superinifinite" and
"outfinity". I have no clue what these terms mean, but they sound like
they should be bigger than infinity.

I tried comparing them on my hands and on my feet but ran out of toes
and fingers. Perhaps some of the other researchers can help me - I'm
at 10 and I still haven't reached the transinfinite numbers :)

calebu2-ga

Omni-infinite

Infinity implies the existence of something from the moment it was
created. Omni infinite was always ... infinite.


Worth a try right? ;-)

SgtCory

Pinkfreud is correct in choosing "transfinite" for its connotation of
the infinities that lie beyond any given infinity.

Georg Cantor's theory of transfinite numbers, which we would today
call infinite cardinals, was significant for demonstrating that there
is more than one "size" of infinity.

The smallest infinity is that of the set of whole numbers, which we
call countably infinite.  Cantor developed a rigorous proof that
become known as his "diagonal" argument, that there are fewer whole
numbers than there are real numbers.

The cleverness of this 19th century argument sparked many important
developments in the 20th century, such as Godel's incompleteness
theorem and Turing's solution of the decision problem for automata.

Unfortunately the burden of such great insight is a heavy one, and
compounded by dirty tricks (of the academic variety) played on Cantor
by jealous colleagues, his mind descended into madness.

Part of Cantor's anxiety was due to his discovery of what we call
today Cantor's paradox. Is there or is there not a largest cardinal
number? Cantor's diagonal argument tells us there cannot be a largest
cardinal number, yet in naive set theory, the cardinality of the
universal set (the set containing all mathematical objects) gives such
a largest cardinal number.

Simplified to its bare bones Cantor's paradox becomes Russell's
paradox (about the set of all sets that do not contain themselves,
which must contain itself if and only if it doesn't contain itself).

There is a related but subtly different paradox of the largest ordinal
number, known as the Burali-Forti paradox. For ordinals there is
indeed a well-defined "infinity plus one" (regardless of what ordinal
you wish to add one to), which is why there cannot be a largest
ordinal. On the other hand in naive set theory one can show that the
set of all ordinal numbers together constitute a largest ordinal
number!

Such paradoxes of naive set theory (strikingly reminiscent of Kant's
18th century "paradoxes" of space and time) gave impetus to the
investigation of the foundations of logic and mathematics, and after
these "gardens of thought" had been properly weeded, to an explosion
of understanding just how infinitely many the infinities are.

regards, mathtalk

The word you are looking for is "transinfinite".