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— the Art of Reasoning
— the Art of Studying Patterns Using Logic
Algebra is the study of,
what I call operational pattern or behavioral patterns.
By operational patterns
I mean patterns that govern action. For example, People who have morining
routines from the time they wake up till they go to work or school have
operational patterns. Some get dressed before they brush their teeth others
have breakfast before getting dressed and brushing their teet. In mathematics,
an operational pattern is for example, the fact that when we multiply two
we can break each number
into two number that together add up to equal its value. In our example,
we can do
Now if we want the
product of the second multiplication to eqaul the product of the first,
we can do
2 x 5 + 2 x
4 + 3 x 5 + 3 x 4 .
Experiencing this behavior
of numbers for hundreds and thousands of years, led people to rule that
(a + b ) x
( c + d ) = a x c + a x d + b x c + b x d .
This is an operational
pattern from mathematical viewpoint.
We can also look at
this pattern as a consistent behavior of numbers. In this sense algebra
deal with the patterns of the behavior of numbers.
are different from patterns of objects such as tiling. In math, patterns
of objects are, for example, the even numbers, the sqaures of the integers
and the prime numbers. While there are operational patterns to generate
all the even number and all the sqaures of the integers, there is no operational
pattern to generate all of the prime numbers.
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Last Update: Nov. 26, 2005