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: 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/
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?
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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