Arithmetic Multiplication Operation

An Arithmetic Multiplication Operation is an arithmetic operation of scaling one Number (the Multiplicand) by another Number (the Multiplier).

• AKA: Multiplication, Multiply, ×, Multiplication Operation.
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• Example(s):
  • [math]\displaystyle{ \times (0,1) \rightarrow 0 }[/math].
  • [math]\displaystyle{ \times (1,0) \rightarrow 0 }[/math].
  • [math]\displaystyle{ \times (1,1) \rightarrow 1 }[/math].
  • [math]\displaystyle{ \times (1,2) \rightarrow 2 }[/math].
  • [math]\displaystyle{ \times (2,2) \rightarrow 4 }[/math].
  • [math]\displaystyle{ \times (1.5,1.5) \rightarrow 2.25 }[/math].
  • [math]\displaystyle{ \times (\frac{1}{9},\frac{1}{9}) \rightarrow \frac{2}{9} }[/math].
  • [math]\displaystyle{ \times (2, (1.3,4)) \rightarrow (2.6,8) }[/math], Scalar-Vector Multiplication Function.
• Counter-Example(s):
  • Arithmetic Addition, Summation Operation, ...
  • Arithmetic Division.
  • [math]\displaystyle{ \times (2,2,2) \rightarrow 8 }[/math].
• See: Proportion Function, Multiplier.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Arithmetic#Multiplication_.28.C3.97_or_.C2.B7_or_.2A.29
  • Multiplication is the second basic operation of arithmetic. Multiplication also combines two numbers into a single number, the product. The two original numbers are called the multiplier and the multiplicand, sometimes both simply called factors.

    Multiplication may be viewed as a scaling operation. If the numbers are imagined as lying in a line, multiplication by a number, say x, greater than 1 is the same as stretching everything away from 0 uniformly, in such a way that the number 1 itself is stretched to where x was. Similarly, multiplying by a number less than 1 can be imagined as squeezing towards 0. (Again, in such a way that 1 goes to the multiplicand.)

    Multiplication is commutative and associative; further it is distributive over addition and subtraction. The multiplicative identity is 1, that is, multiplying any number by 1 yields that same number. Also, the multiplicative inverse is the reciprocal of any number (except 0; 0 is the only number without a multiplicative inverse), that is, multiplying the reciprocal of any number by the number itself yields the multiplicative identity.

    The product of a and b is written as a × b or a·b. When a or b are expressions not written simply with digits, it is also written by simple juxtaposition: ab. In computer programming languages and software packages in which one can only use characters normally found on a keyboard, it is often written with an asterisk: a * b.

2009

• http://www.isi.edu/~hobbs/bgt-arithmetic.text
  • We will not need multiplication in other chapters, but we need to introduce it here because we will need it in defining proportions and half orders of magnitude.

    Multiplication is defined in a manner similar to addition. The predication "(product n1 n2 n3)" means that n1 is the product of n2 and n3.

    The product of a number n and zero is zero.

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