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The definition I had given for this word (one of several numbers which are infinite but not equal to each other) actually defines "transfinite number". The whole topic is very esoteric; no short definition will make much sense to anyone not in the field of mathematics. 10:20, 28 July 2005 (UTC) (aka pol098)

Actually, 'transfinite' just means 'beyond finite', in a strict sense. --Wytukaze 10:33, 28 July 2005 (UTC)
If transfinite means beyond finite, then transfinite is effectively a synonym for infinite. I don't know that transfinite has ever been used in any other context than mathematics.

In mathematics, there are several numbers, all of them infinite in that they are larger than any number you can write, but not equal to each other. They are called aleph-0, aleph-1, etc. These numbers are called transfinite numbers. But I think this is the only use of transfinite; it is an adjective, not a noun, and hence cannot be 'A transfinite number', nor can it be a definition I had used a few revisions ago. All the correct definitions I thought of were very clumsy, something like 'adjective qualifying number to express that it is one of a class of numbers which are infinite but distinct from each other'

So I would prefer to go back to a previous definition of mine, which merely cross-references to 'transfinite number'.

I don't think I should do this myself; if others agree, the entry should be edited; if I'm being too pedantic, ignore this.

There's more about this interesting topic in Wikipedia (I haven't read it), and in 'Lecons sur les nombres transfinis' by Waclav Sierpinski (probably out-of-date now). 14:18, 28 July 2005 (UTC) (but I contribute as pol098 if I make sure I'm logged in)

The point of Cantor's work was to establish that there are several kinds of infinity. Eclecticology 17:09:44, 2005-07-28 (UTC)
You're right about the latter part of my definition; it can't be 'a transfinite number' in an adjective sense, and that was a mistake on my part. The current definition that is there, "relating to transfinite numbers" is satisfactory. However, that is not the only definition of transfinite; as with many mathematical terms, there is a lay usage as well, finite and infinite being cases in point. Hence, I am happy with the current definitions as currently laid out. --Wytukaze 20:41, 28 July 2005 (UTC)