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I had trouble phrasing a recent question because I couldn't find simple wording to convey the difference between languages like English where all kinds of numbers are expressible, such as "nineteen thousand four hundred and sixty two" and other languages like most Australian Aboriginal languages with only a very basic or minimal number system that typically have only "one", "two", and "three".

Perhaps Wikipedia says it better than I could:

Not all languages have numeral systems. Specifically, there is not much need for numeral systems among hunter-gatherers who do not engage in commerce. Many languages around the world have no numerals above two to four—or at least did not before contact with the colonial societies—and speakers of these languages may have no tradition of using the numerals they did have for counting. Indeed, several languages from the Amazon have been independently reported to have no numerals other than 'one'. These include Nadëb, pre-contact Mocoví and Pilagá, Culina and pre-contact Jarawara, Jabutí, Canela-Krahô, Botocudo (Krenák), Chiquitano, the Campa languages, Arabela, and Achuar. Many languages of Australia, such as Enindhilyagwa and Warlpiri, do not have words for quantities above two, as did many Khoisan languages at the time of European contact. Such languages do not have a word class of 'numeral'.

Please note I'm trying to make value judgements about individual languages, just looking for the best way to describe these two culturally and/or linguistically different approaches to number.

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The WP statement was wrong about Anindilyakwa (I've changed it), the language has terms for words up to twenty, just that they're not being learned by kids anymore. –  Gaston Ümlaut Oct 5 '11 at 6:56
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I'm not sure there's a specific term for this. I myself (a linguist) would call such a system an open-ended numeral system. Rather than describing what a language can't do, we normally describe what it does, so we talk about a language having a system for expressing numerals up to a certain point. I've worked on languages that have an upper limit of 3, and on one that had an upper limit of 99 (ie no word for 100).

BTW, English doesn't really have words for all numbers, there's always an upper limit, so while there is a technical jargon in mathematics for referring to any number, everyday English does not have names for every number.

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What are you referring to in your last paragraph? –  Alenanno Oct 2 '11 at 13:19
regarding English, how about stuff like: one thousand two hundred thirty four billion billion billion? Theoretically this can cover all integers –  Louis Rhys Oct 2 '11 at 13:20
@Gaston: That's why I tried to talk about "number system" rather than "word for every number". –  hippietrail Oct 2 '11 at 13:25
@Alenanno Well first we have to think about what we mean by "a name for a number". We have a system to express any number (e.g 1x10^6 is a million), but don't have names for all the numbers. Think about googol: the name for the number expressed as 1x10^100. Large number, but there are bigger numbers. Ok, lets get bigger. Googolplex: 1x10^Googol. That's pretty big. But there are even bigger numbers! So many, in fact, that 1x10^Googolplex doesn't come close. Point is, the natural numbers are infinite. We can express any of them, but we haven't named them. –  Nathan Oct 2 '11 at 15:15
@Nathan Ah yeah, that's right... Thanks for taking the time to comment. :D –  Alenanno Oct 2 '11 at 15:29
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These are often closely related to Approximate Number Systems. Piraha for example, in claimed to have just the numbers 1 and 2. But when they use them, it appears that they use even these small numbers in an approximate manner (2 can refer to some single thing that is unusually large).

I've heard that many of these language with numbers say, 1-7 actually have an approximate number system, more akin to "single, pair, a few, a lot" With the right scenario a field linguist could ask an English speaker, "How many apples are on the table?" And the subject would say "A few" and the linguists would record, "Ah, so 'a few' is the number 3."

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