One over infinity: what's the name for the fraction?

[QUOTE=Mathochist]
Infinity isn’t an ordinal. ω is an ordinal.
[/QUOTE]

Well, yes, that’s the point. The pattern is that “1/cardinal” is pronounced “one ordinal.” What’s the ordinal corresponding to the cardinal infinity? I suppose 1/infinity could be pronounced “one omega,” but which takes precedence as an answer to the OP, math or the language?

And welcome back.

[QUOTE=Indistinguishable]
Wow, welcome back Mathochist.
[/QUOTE]

Thanks Indistinguishable. Hopefully Bowling Green, KY will take less of my time than New Orleans, LA did.

[QUOTE=foolsguinea]
1 / infinity is “an infinitesimal amount.” I always thought that was the definition of infinitesimal.
[/QUOTE]

In a sense; that’s certainly a useful definition in many cases. But, like everything else, the concept really has not one sharp definition for all purposes, but a variety of different ones appropriate in different contexts, related through family resemblances, of course. One ultra-nitpicky point is that it’s often useful to treat 0 as an infinitesimal, without postulating that 0 is the inverse of any infinite quantity. Slightly less nitpickily, but along the same lines, there are systems of non-standard analysis (such as Lawvere’s smooth infinitesimal analysis, as opposed to the more well known Robinson-style approach) where the infinitesimals don’t reduce to triviality, but infinitesimals generally don’t have (and thus aren’t) reciprocals; thus, in such systems, to be an infinitesimal quantity cannot be simply the same as to be the reciprocal of an infinite quantity, and a different definition has to be used (e.g., a quantity which, no matter how many times you add it to itself, will never become greater than 1).

[QUOTE=Topologist]
Well, yes, that’s the point. The pattern is that “1/cardinal” is pronounced “one ordinal.” What’s the ordinal corresponding to the cardinal infinity? I suppose 1/infinity could be pronounced “one omega,” but which takes precedence as an answer to the OP, math or the language?

And welcome back.
[/QUOTE]

Thanks.

And to vary the theme: Infinity isn’t a cardinal. א[sub]0[/sub] is a cardinal.

Also Angelo Sodano :smiley:

My browser gets amusingly confused trying to reconcile right-to-left Hebrew with a subscript from the typical left-to-right universe. Am I the only one who sees the zero appearing on the left of the aleph?

[QUOTE=Mathochist]
Infinity isn’t an ordinal. ω is an ordinal.
[/QUOTE]
Boobies are ordinal?

[QUOTE=Indistinguishable]
My browser gets amusingly confused trying to reconcile right-to-left Hebrew with a subscript from the typical left-to-right universe. Am I the only one who sees the zero appearing on the left of the aleph?
[/QUOTE]

It happened to me too…

testing: א [sub]0[/sub]

nope. I always said we need LaTeX on here. I’ve got it on my weblog, so why not here!

[QUOTE=Cervaise]
Boobies are ordinal?
[/QUOTE]

Some of them are extraordinal!

Hmm, are you by any chance Unapologetic?

[QUOTE=Capt. Ridley’s Shooting Party]
Hmm, are you by any chance Unapologetic?
[/QUOTE]

What gave me away? The fact I list it in my SMDB profile? :wink: