# Why does our system of numbers include 11, 12 and all the teens?

Asked by rojo (24179) April 22nd, 2017

I understand our commonly used numbering system is a denary or base ten system. That is you go from 0 to 9 and then begin on the next level and that holds true for the first ten numbers and then all numbers from twenty up (until we get to 111 but that is also part of the problem.

So, let us start at 0, then 1, then 2 etc all the way to 10.

BUT the numbers after 10 breaks with the system and is called ELEVEN, then TWELVE and then we get into seven other oddball numbers called the “TEENS”.

Why?

Why does it not stick to the system? Why is 11 not called Ten-one and 12 not called Ten-two, and 13 not called Ten-three the way the rest of the system works?

Or, for that matter and for consistency, why isn’t 10 called “Tenty” and thus have Tenty-one, Tenty-two and so forth

Or conversely, why is 30 not called Twenty-ten, 31:Twenty-eleven; 32: Twenty-twelve and so on up to 40 when we start over again with Forty-one through Forty-nineteen? (although, technically 40 should be 30 but let’s save that for a different question).

Maybe this is just my CDO getting to me but it is really bothering me.

Observing members: 0 Composing members: 0

OR why, at least is 11 and 12 not called “Eleventeen” and “Twelveteen”.
and if you did that, why is it “Ten” and not “Teen” in the first place.

What is wrong with this world!

rojo (24179)

Illiterates began the system, nobody ever bothered changing it.

Patty_Melt (17514)

Caesar changed the calendar (not that he did a good job, I mean why not have it based on a lunar calendar with 13 – 28 day months with a party day at the end of the year) and all they had were I’s, V’s, and X’s with a few M’s and C’s thrown in for good measure.

Surely someone could have done better.

rojo (24179)

Back then, maybe. Now, undoubtedly.

Patty_Melt (17514)

@Patty_Melt pretty sure who ever came up with the number system was anything but illiterate. It’s genius, actually. Same with our writing system.

Well, when you say “teen,” I imagine that stands in for the “ten.” I don’t know why 11 and 12, but I’ve wondered that myself.

Dutchess_III (46938)

Numbers that are used more often tend to have more irregular names.

“Teen” has the same root as “ten”, so thirteen does ultimately mean “three ten”, but its form is irregular.

The origin of “eleven” and “twelve” isn’t entirely clear, but it probably comes from “one left” and “two left”, as in one and two left over from ten.

DominicY (5662)

From thefreedictionary.com: [0]

“Word History: It is fairly easy to see how the words for the numbers thirteen through nineteen are related to the numbers three through nine. The thir- in thirteen, for example, sounds somewhat like three, and the suffix – teen resembles ten. But what about the words eleven and twelve? Eleven doesn’t sound anything like one, and although twelve is spelled with the same tw- found in two, twice, and twin, what is the – elve? English probably inherited all the words for the numbers eleven through nineteen from Germanic, the protolanguage that is the common ancestor of English and its close relatives, the other Germanic languages like Dutch, German, and the Scandinavian languages. The English words that end in – teen descend from compounds formed in the Germanic protolanguage from the words for the numbers three through nine added to a form of the Germanic word for ten. This form of the word for ten eventually evolved into Modern English – teen. The Modern English words eleven and twelve descend from ancient Germanic compounds, too, and the speakers of the Germanic protolanguage would have recognized the meaningful parts of the compounds just as easily as English speakers recognize the meaningful parts of thirteen and fourteen. Modern English eleven descends from Old English endleofan, and related forms in the various Germanic languages point back to an original Germanic compound *ainlif, “eleven.” *Ainlif is composed of *ain-, “one,” the same as our one, and the suffix *- lif from the Germanic root *lib-, “to adhere, remain, remain left over.” Thus, eleven is literally “one-left” (over, that is, past ten). Similarly, twelve comes from an ancient Germanic *twalif, “two-left” (over past ten). However, as Germanic evolved into Old English, and Old English into Modern English, changes in pronunciation obscured the meaningful elements in these compounds so that it was no longer possible to see how eleven was related to one.”

From dictionary.com: [0]
n.
c.1200, elleovene, from Old English endleofan, literally “one left” (over ten), from Proto-Germanic *ainlif- (cf. Old Saxon elleban, Old Frisian andlova, Dutch elf, Old High German einlif, German elf, Old Norse ellifu, Gothic ainlif), a compound of *ain “one” (see one ) + PIE *leikw- “leave, remain” (cf. Greek leipein “to leave behind;” see relinquish ).

http://www.etymonline.com/index.php?allowed_in_frame=0&search=eleven

1) To make a comparison, German words for 11 and 12 are elf and zwölf _, while -teen is quite similar to German _zehn (ten), which is used to from numbers past 12, dreizehn, vierzehn, fünfzehn…
2) Other languages have the system similar to the one you proposed. Slavic languages use words that can be translated as “one-nine on ten”, in Proto-Slavic “edin-devent na desenti” (kinda). Spanish once is derived from Latin undecim, which is derived from PIE *óynom déḱm̥t, which meant “one on ten” or “one plus ten”.
3) Why don’t we call 30 Twenty-ten? Simply because twenty istelf is not a distinct unit, but “two tens”. When it comes to numbers, you have several distinct units: one-nine, ten, one hundred, one thousand, one million. All other numbers are combinations of “a set of distinct units”. Thus, 20 is “two-ten” 30 “three-ten”, 128 “one hundred two-ten and five” and so on.

Sneki95 (7017)

addition: I think French has a different system of numbers, but I’m not sure.
and *form, not from numbers
“one hundred two-ten and eight

Sneki95 (7017)

Interesting question. Even in Spanish 11,12,13,14, and 15 are their own words, then 16–19 have a derivative word for ten plus the word for 6, 7, 8, and 9.

In English once you hit the number 13 the teen is like ten, but in Spanish it doesn’t start until 16.

JLeslie (65558)

^ It’s actually the same system, just used differently.

once, doce, trece, catorce, quince = from Latin

dieciséis, diecisiete, dieciocho, diecinueve = from Spanish (the non-Latinized old language) “diez y X”. Or from the “modern” one, not sure. Surely not borrowed from Latin.

Both systems mean “X plus ten”

Which is exactly what you said. Sorry.

Sneki95 (7017)

^^Right, but diez y X, or actually dieciX doesn’t begin until 16, while in English it’s 13.

In Spanish the dieci is in front of the number same as 20’s and 30’s, but in English the 10’s we put the “teen” at the end of the word, while 20’s and 30’s, etc. it is at the front.

JLeslie (65558)

^Yup. Some languages use the “ten+one”, while the other use “one+ten”.
When it comes over twenty, then you can combine the systems, and say “six+ ten”, but then say “twenty+ one”. (German, however, uses einundzwanzig, which is “one + twenty”)
I’ve no idea why, but it happens.
And it’s cool.

I love this question so much.

Sneki95 (7017)

There are always little quirks in languages. Another in Spanish is 200, 300, 400, 600, 700, 800, 900 all start like 2,3,4,6,7,8,9 plus 100, but 500 sounds like the word for 15 plus 100. I don’t know if that happens in other languages.

JLeslie (65558)

@JLeslie Oh, yeah I remember that. My Spanish teacher always had to remind us how to say 5, 15, 50 and 500. No one could remember it from the start. Spanish have some bone to pick with fives, it seems. I don’t know if other languages do anything similar.

Sneki95 (7017)

And then the French get into “quatre-vingt et onze” for 91.

zenvelo (39491)

Part of the reason may be related to why the most common verbs tend to be irregular. It was only after people came up with the most common verbs that the language evolved to use a common set of rules for conjugating new verbs. Similarly, it may be that there were common names for numbers from 1 to 19 and only later did people decide to regularize the names given for higher numbers.

I have been thinking about this obsessively and I think the problem is not with 11 or 12 but with 10.

Ten should have been Onety (or something similar) and then 11 would have been Onety-one and 12 Onely-two which would then have made sense with the rest of the system.

So, somewhere down the line a mistake was made. Or, perhaps it was purposely chosen to be different. The question is why?

Even if as @JLeslie points out 13 – 19 are a derivative of 10 plus another number, that does no explain why we are looking at 3 PLUS 10, etc., as opposed to the rest of the numbers where we have, for example, 20 PLUS 3 or 30 PLUS 3. Why are the teens backwards when compared to the rest?! And that still doesn’t explain the oddballs 10, 11 & 12.

What would happen if our entire system was derived from Base 20 instead of Base 10? What mysteries would be solved if we used this as our unit of measure?

rojo (24179)

@rojo The onety probably should be tenty. It’s not a ones place, but a tens place. Or, maybe 1–19 should all be its own number, and not start the twenty, thirty, until the twenties.

Maybe they didn’t count very high for most things back in the day and didn’t need the simplicity of 20+X and 30+X very often?

I also was thinking about the word dozen. Does that occur in many languages? A separate word for twelve? Or, is that just based on America using a twelve count for packaging? Dozen, case, we have a few alternatives for numbers. Also, baker’s dozen. My husband hates when people use the terms dozen or half dozen, maybe Spanish doesn’t have those words, or maybe his family doesn’t use them readily if they exist.

Edit; I just googled and it looks like Spanish does have an equivalent to dozen it’s docena.

JLeslie (65558)

@rojo But ”-ty” ultimately means “ten”, so “onety” would just be “one ten”; seems redundant.

DominicY (5662)

Should be “one zero.”

Dutchess_III (46938)

@DominicY No, one ten would be correct if your system is based on 10 numbers (0 – 9) because at that point you start over your groupings. @Dutchess_III is correct it would be 1–10-0 and 11 is 1–10-1, 12 is 1–10-2 just as twenty is 2–10-0 and 21 is 2–10-1 etc.

rojo (24179)

The names one through ten predate the decimal system. It was just a way of assigning a different name to the numbers we could count on our hands. Note that digit is also a name for finger. It was only later on that the need was seen for systematic nomenclature.

But it could have something to do with what @JLeslie mentioned. English money used to incorporate the number 12; twelve pence being a shilling while sixpence was exactly what is is called. But then if I remember right it got complicated with a florin being two shillings (24p); half a crown being 2½ shilling or 30p and a crown being 5 shilling (why not six or twelve?). But the numbers are Arabic. Do Arabic counting systems have a number for 11 or 12 that is individually named and not a combination of 10 plus something?

rojo (24179)

@LostInParadise do the numbers 11 & 12 also predate the decimal system? Is that where part of the confusion comes in?

rojo (24179)

I guess I could fall back on the way they taught us to count at College.

Q: How does an Aggie count to 10?

A: 1, 2, 3, 4, 5, and another, and another, and another….....

rojo (24179)

One zero = 0, not 10.
Besides, we got zero much later than other numbers, if I’m correct. There was no time for ye olden ones to come up with a word for zero.

Sneki95 (7017)