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### Counting in the Teens

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Date: 09/10/98 at 15:05:20
From: Alisha
Subject: Counting in the teens

I take Algebra 2, and one of the question we need to know the answer
to is why, when you count, you go ten eleven twelve thirteen instead
of ten eleventeen twelveteen thirteen.

I have looked everywhere for an answer.
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Date: 09/11/98 at 12:08:01
From: Doctor Peterson
Subject: Re: Counting in the teens

Hi, Alisha,

There's a fascinating discussion of this question (and some others
like it) in the math-history-list:

http://mathforum.org/kb/message.jspa?messageID=1375416

Look especially at the messages by John Conway; he discusses this also
in his book _The Book of Numbers_.

Here's his answer on eleven and twelve:

There seems to be a natural tendency in language for the first
few terms of a sequence to be treated specially.  Thus in English,
"eleven" is really "one left (over)",  and "twelve" is "two left",
so that the implied "after ten" is omitted. But from thirteen on
it seems that we should explicitly mention the "ten", since we're
getting so far away from it that we might otherwise forget it!

So the "e" in eleven means "one", and the "tw" in twelve means "two"!

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```

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Date: 09/11/98 at 15:14:05
From: Alisha
Subject: Re: Counting in the teens

Thank you for your answer to my question.

Alisha
```

```
Date: 03/12/2003 at 20:12:27
From: Karen
Subject: The origin of numbers

What are your thoughts on the origins of the names for 11, 12 and 20?
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Date: 03/12/2003 at 22:44:52
From: Doctor Peterson
Subject: Re: The origin of numbers

Hi, Karen.

You can find more on this in a good dictionary, and in various books
specifically dealing with the history of numbers.

In _Mathematics: From the Birth of Numbers_, Gullberg says this:

Eleven is a derivative of Old English _endleofan_, where the
terminal -fan is believed to carry the meaning of "to leave"
or "left", that is, _one left_ after counting ten (fingers).

Twelve has developed in a similar manner from Old English _twelfe_
meaning _two left over_ after counting ten; it may be more clearly
seen from the Gothic _twailif_.

Twenty was _twentig_ or _twegentig_ in Old and Middle English,
where twen and twegen were forms meaning two, and the suffix -tig
recalls German -zig.

Merriam-Webster, at m-w.com, has this to say on the etymology of the
words:

Eleven
Middle English enleven, from enleven, adjective, from Old English
endleofan, from end- (alteration of An one) + -leofan; akin to Old
English lEon to lend

Twelve
Middle English, from Old English twelf; akin to Old High German
zwelif twelve, Old English twA two, -leofan (as in endleofan
eleven)

Twenty
Middle English, from twenty, adjective, from Old English twEntig,
noun, group of 20, from twEn- (akin to Old English twA two) + -tig
group of 10; akin to Old English tIen ten

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Elementary Math History/Biography
Elementary Number Sense/About Numbers
Middle School History/Biography
Middle School Number Sense/About Numbers

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