[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 
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? 