Abarim Publications' online Biblical Greek Dictionary
The noun αριθμος (arithmos) means number. However, where in our modern world the word number may mean something abstract and theoretical, in the classical world there wasn't much in terms of number theory. In fact, number theorists were a sectarian minority, and most people regarded numbers rather as words, which is why there are no numbers in the Bible (apart perhaps from 666 or χξς, ch-x-s, as used in Revelation 13:18) and all numbers are words like any other words spelled in letters.
In recent antiquity, there was no numeracy (number-literacy) the way we moderns commonly have it. A number was a word like any other word, that helped an observer make sense of things; real things that were observed in obvious reality. It was akin a word like category, in that a category like, say, "apples" would contain, say, eleven of them. Such a distinction would allow an observer to compare apples with, say, oranges, of which she had, say, nineteen, which was obviously about twice as many. But, particularly where larger numbers were concerned, words like εκατον (hekaton), a hundred, or χιλιοι (chilioi), a thousand, were basically synonyms for a lot and a great many.
Our hallowed English word mathematics comes from the Greek verb μανθανω (manthano), meaning to learn (the Biblical word for disciple is μαθητης, mathetes, learner). And although from our noun αριθμος (arithmos) comes our English word arithmetic (the study of how quantities relate), the word αριθμος (arithmos) itself comes from the same Proto-Indo-European root "hrey-", meaning to think or arrange, from which come our English verbs to ready (to lay out handy) and to rhyme (to conveniently group statements; rhyming probably originated as a mnemonic aid), and possibly the words rite and ritual (to remember by repetition; a ritual is supposed to have the deep thoughts of one's hearts bubble to the conscious surface).
The core idea behind the noun αριθμος (arithmos) is that of clear definition and discernment. Things can only be numbered when they can be clearly distinguished from other such things and from the background. Numbers go hand in hand with borders and with definitions, and the same thing goes for the names of things: things can only be named when they are clearly distinguished from other things (hence Genesis 2:19-20 and Judges 13:18; see ονομα, onoma, name or noun), which is why stars are so hard to count (Genesis 15:5). The whole idea of science is precisely that: to distinguish things from other things (see the verb σχιζω, schizo, to break, split or divide). That means that the "number" to which believers were added (Acts 16:5) was much rather a single social entity clearly distinguishable from society at large, than some actual amount of humans within a larger population of largely similar humans.
The noun αριθμος (arithmos), number, is used 18 times in the New Testament, see full concordance, and from it derive:
- Together with the familiar particle of negation α (a), meaning not or without: the adjective αναριθμητος (anarithmetos), meaning innumerable (Hebrews 11:12 only, but also see Revelation 7:9). Contrary to popular belief, this word does not speak of amounts so great that anybody would lose count, but rather about things that have no clear boundaries, no clear definitions or no obvious names. Or perhaps they have them but the observer isn't privy to them. Things can only be numbered when both their limits and their similarities with other things are obvious, and when they are not, they can't be numbered.
- The verb αριθμεω (arithmeo), meaning to number (but not so much to count): to reckon things by their limits and their close similarities to other identical things (Matthew 10:30, Luke 12:7 and Revelation 7:9 only). Another way to define this verb is to disregard whatever may set one thing apart from a similar thing: to disregard the defining uniqueness of similar things. From this verb derives: