Exploring the Use of Abbreviations in Mathematics: Why is a x b Written as ab?

[Cheman]

Why is a x b written as ab? Is it just for the purpose of abbreviation so you don't have to write as much or because the multiplication sign could be mistaken for a letter x?
Thanks.

 

[enigma]

The 'x' holds a special meaning for multiplication of vectors: The Cross Product

It's also possible to mistake it for the letter x.

 

[Muzza]

People are lazy, and it's "a lot" easier to write $$ab$$ instead of $$a \cdot b$$ or $$a \times b$$.

 

[pnaj]

To go along with enigma wrote, when I saw your question in the list, I assumed that you were talking about vectors and the cross product!

 

[gravenewworld]

As my genious high school calc teacher always used to say, "Good mathematicians are notoriously lazy." And its true. Its just written that way out of convention to save the effort of having to write the x. I don't think that x is "reserved" for the cross product. I mean lots of symbols have 2 meanings you can tell which is referred to by context. For example l l is used to mean absolute value in some cases and it is also used to denote the order of a group.

 

[Galileo]

I don't think good mathematicians are lazy. Anyone who has ever gotten anywhere must have worked hard for it and I`m sure that's true for all mathematicians in history. It's just that mathematicians work hard to make things as easy as possible so they can be lazy :P

 

[Zurtex]

People are lazy, and it's "a lot" easier to write $$ab$$ instead of $$a \cdot b$$ or $$a \times b$$.

And $\cdot$ is supposed to be the decimal place and $.$ is supposed to be the multiplication symbol, but people just forget out of ease of writting.

 

[TALewis]

This page talks about the origins of different symbols for math operations:

http://members.aol.com/jeff570/operation.html

From the first section on multiplication:

By juxtaposition. In a manuscript found buried in the Earth near the village of Bakhshali, India, and dating to the eighth, ninth, or tenth century, multiplication is normally indicated by placing numbers side-by-side (Cajori vol. 1, page 78).

Multiplication by juxtaposition is also indicated in "some fifteenth-century manuscripts" (Cajori vol. 1, page 250). Juxtaposition was used by al-Qalasadi in the fifteenth century (Cajori vol. 1, page 230).

According to Lucas, Michael Stifel (1487 or 1486 - 1567) first showed multiplication by juxtaposition in 1544 in Arithmetica integra.

In 1553, Michael Stifel brought out a revised edition of Rudolff's Coss, in which he showed multiplication by juxtaposition and repeating a letter to designate powers (Cajori vol. 1, pages 145-147).

 

[Zorodius]

It's an intuitive notation. 3b seems to imply you have three b's. ab seems to imply you have a b's.

I don't think good mathematicians are lazy. Anyone who has ever gotten anywhere must have worked hard for it and I`m sure that's true for all mathematicians in history.

No doubt, but it gets an easy laugh out of a class full of students who resent math.

 

[sunny86]

hehehe..in my opinion , as the process on solving the mathematic problem may take long solution and applying many formula . To avoid confusing and easy to solve , so the mathematicians introduce those symbol to make the job easy.
e.g :
pai = 3.142...
a x b = a.b = ab ( multiplied )
.
a -- b = a/b ( divided )
.

p/s : sorry i not really know on using computer and don't know where to find all those mathematics symbol...sorry.. :rofl: