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Counting in the Teens

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. 
Could you please help? Thanks.

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:   

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   

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

Thank you for your answer to my question.


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?

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, has this to say on the etymology of the 

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

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

  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   
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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