Multiplying by 1Date: 09/01/98 at 13:04:40 From: Rizwan Abbasi Subject: Multiplying by 1 Dear Dr. Math, My question is as follows: Multiply means increase in number. When 1 is multiplied by 1, the answer is 1. The answer is 1. Why is it? Each one independent unit is being multiplied but the number is not increased. Looks erratic to me. Please define. Yours truly, Ehsanullah Abbasi Date: 09/01/98 at 17:35:56 From: Doctor Rick Subject: Re: Multiplying by 1 Hello, Rizwan. This is an interesting question, and I can make it seem even stranger. Not only can you multiply by 1 and the result does not increase, but you can also multiply by 1/2 and the result is smaller. If you look at the original meanings of words, the same problem arises with the word "add". It comes from the Latin "addere" meaning "to give to." Yet I can add a negative number, with the result that something is actually taken away. I think the same sorts of problems will arise in any language, and in other disciplines besides math. A word that means one thing in everyday language will have a somewhat different meaning, or a very specific and specialized meaning, in math or physics or economics or another specialized field of study. When people have a new idea or invent a new product, sometimes they invent an entirely new word to identify it. But sometimes they just use an existing word that has a similar meaning. For instance, an electrical current is like a current in a river, but it is not exactly the same. The basic words of math like "multiply" and "add" were adapted from everyday life long ago. Back then, concepts like negative numbers and even zero had not been developed. People would really only think in terms of multiplying by positive whole numbers. And why bother to multiply by 1? It doesn't do anything. So the use of the words made sense. But mathematicians gradually extended the meanings of the words. Not only can you multiply fractions or negative numbers, you can multiply matrices or numbers in modular arithmetic where the idea of one number being greater than another is meaningless. The things that we call "multiplication" today have a lot in common with simple multiplication by an integer greater than 1, so it makes sense to use the same word for them. Why invent a new word just because the original narrow meaning of the word doesn't fit any more? In short, the problem that you have raised is a reason for the existence of specialized dictionaries of science and technology. If you look up the meaning of a word in a dictionary of everyday language and try to apply the definition to the way the word is used in a specialized field like math, you will often only get confused. Just use a word the way it is defined in the field you are working in, and don't worry about what it means in everyday life. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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