Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Almost infinite
Replies: 19   Last Post: Mar 21, 2013 2:40 PM

 Messages: [ Previous | Next ]
 David R Tribble Posts: 3,426 Registered: 7/21/05
Almost infinite
Posted: Dec 11, 2012 10:58 PM

We see the phrase "almost infinite" (or "nearly infinite", or "infinite
for all practical purposes") in much literature for the layman, usually
to describe a vastly large number of combinations or possibilities from
a relatively large number of items. For example, all of the possible
brain states for a human brain (comprising about 3 billion neurons), or
all possible combinations of a million Lego blocks, etc.

Obviously, these are in actuality just large finite numbers; having an
infinite number of permutations of a set of objects would require the
set to be infinite itself, or the number of possible states of each
element would have to be infinite. Most uses of the term "infinite
possibilities" or "almost infinite" are, in fact, just large finite
numbers. All of which are, of course, less than infinity.

But is there some mathematically meaningful definition of "almost
infinite"? If we say that m is a "nearly infinite" number, where
m < omega, but with m having some property that in general makes it
larger than "almost all" finite n?

Personally, I don't think there is such a definition; but then I would
enjoy being proved wrong.

-drt

Date Subject Author
12/11/12 David R Tribble
12/11/12 William Elliot
12/12/12 fom
12/12/12 William Elliot
12/12/12 fom
12/12/12 ross.finlayson@gmail.com
12/17/12 Porky Pig Jr
12/12/12 Richard Tobin
12/13/12 Jim Burns
12/13/12 forbisgaryg@gmail.com
12/16/12 David R Tribble
12/17/12 Calvin
12/17/12 netzweltler
12/17/12 Calvin
12/17/12 netzweltler
12/13/12 FredJeffries@gmail.com
3/17/13 fom
3/17/13 fom
3/21/13 Frederick Williams
3/21/13 scattered