Algebra/Arithmetic
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Arithmetic is the process of performing certain operations on numbers or variables. There are four arithmetic operations possible namely addition, subtraction, multiplication, division.
Contents |
[edit] Addition
Refer Wikipedia's article on Addition
To define the number one is a rather difficult task, but we all have a good intuitive sense of what "oneness" is. Oneness is the property of having or thinking of a singular quantity, i.e. you have one dollar, one bushel of potatoes, or one light year. From here we can recursively define the natural numbers by assigning a new name for each new number of unities that we have:
1 : unity : one
2 : 1 + 1 : two
3 : 1 + 1 + 1 : three
.
.
.
n : 1 + 1 + ... + 1 : n ones
Now that we have named the numbers we can define addition as the process of counting how many unities we have, i.e.
[edit] Subtraction
Refer Wikipedia's article on Subtraction
Subtraction can likewise be defined as counting initial quantity of unities and removing some amount, i.e.:
implies 5 unities remove three unities, leaving a result of two unities.
[edit] Multiplication
Refer Wikipedia's article on Multiplication
Multiplication is a shorthand for addition, i.e.
What this means is to add up three five times; or add up five three times.
[edit] Division
Refer Wikipedia's article on Division
The above division problem asks the question if six is 1+1+1+1+1+1, and three is 1+1+1, then how many sets of three can we break six into? The answer is of course 2, i.e.
; two sets of three.
Note: Division is the first operation where a problem arises. In all the previously defined operations (addition, subtraction, and multiplication) we could perform the operation on any pair of numbers we chose. However, with division we cannot divide by zero. Much will be said about this fact throughout the course of this book, and even through your studies in all of mathematics.
