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

One over two (1/2) is one half.

One over three (1/3) is one third.

One over one hundred (1/100) is one one-hundredth.

And so on.

What’s the word or term for one over infinity? One infinitieth?

It’s undefined. Infinity isn’t a number. What’s 1/purple?

Well, it depends on how you define one over infinity, but with one kind of definition it would be “zero”.

Right, get more specific about the system you’re working with and we can talk. In something like, say, the projectively extended real numbers, with a single unsigned infinity, the answer would be 0. In something like IEEE floating-point, with signed infinities (and signed zeros), the answer would be the zero of corresponding sign. In something like the surreal numbers, the answer would be “Well, there are a lot of different numbers around which deserve to be called ‘infinite’. Which one do you want to take the reciprocal of?”. And, in something like the plain-vanilla real numbers, the answer would be “Well, infinity isn’t actually one of the numbers, so… it’s like 1/purple.” So, it all depends on what system you’re working within.

But, your question seems to be more of a linguistic one than a mathematical one. As far as forming the word goes, the process seems largely regular (beyond the denominator 2, anyway; interesting things often seem to happen with the number two): take the ordinal name of the denominator and preface it with “one” (or whatever the numerator may be). And there seems clear precedent that “infinitieth” serves as the appropriate ordinal name, so, yeah. I suppose “one infinitieth” would be about right, to such extent as anyone would want to say such a thing.

Zero?

… or at least close enough.

With the caveat that you need to specify what system you’re working in, you might call it in an infinitesimal.

One purpleth.

1 purpleth. Duh

ETA: One ought not keep one’s reply window open too long.

Exactly. This is a fill-in-the-blank construction in English. The only one that has a special name is “one half.” After that, they’re all in the format of “one ordinal.” Since all the ordinals after third are -th constructions, the answer to the original question is “one infinitieth.”

The question was definitely language oriented, rather than mathematical. I wondered if there was a standard colloquial term for one infinitieth that wasn’t “one infinitieth.”

Which I suppose makes one over pi “one pieth.”

Kind of correct, but to nitpick, there are “twenty-first” and such things, of course.

And what’s 1/eternity? Eternieth?

The length of a vacation.

1 / infinity is “an infinitesimal amount.” I always thought that was the definition of infinitesimal.

http://en.wikipedia.org/wiki/Infinitesimal

There you go. Ignorance fought.

Valid points both, but the larger point still stands despite these exceptions.

Well, as Indistinguishable says, it depends on what number system you’re using. But the real numbers do not contain infinitesimal elements.

Infinity isn’t an ordinal. ω is an ordinal.

Wow, welcome back Mathochist.