The Adventures Of Aleph-Null

Roberta X referred to Aleph-Null in a post last Friday:

● Linguistic Patrol: At&T (I love you guys, O Providers of my Internet, POTS and Celphone, please don't pull the plug, 'kay? Call me?) keeps stickin' Post-Its™ to the newspaper that read "When you need more than 411, call the new 411." No, dammit, "411" was the number for the old 411. Or is black the new black? "When you need a number more than five, use five." Look, that only works with Aleph-null (et seq...) and I am not sittin' here with my steam-powered desk phone waiting for the dial to scroll back, flipping the pulse contacts a transfinite number of times, okay?

Now it sounds to me like she might be referring to a place that only exists in Science Fiction, so I inquired and she was kind enough to explain:

Transfinite Maths Made Stupid, with your hostess, Dr. X:

Aleph-null is the, erm, smallerest transfinite number.

From Wikipedia: "...m is a transfinite cardinal. That is, there is a Dedekind infinite set A such that the cardinality of A is m.
"m + 1 = m." Or m + 10. Or m + 100. And so on, though not exactly forever.

And that's the only sensible situation that came to mind in which "411" = "the new 411," other than for extremely small values of "new" which would appear to be ruled out by the emphasis given the greater utility (and implicitly, more content) of the "new 411."

OTOH, advertising has been driving the value of "new" near zero for over a century...

I laughed till I cried. This is why I read Roberta's blog.