why an set of integer denoted by z
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An integer can be denotated by any letter. Teachers/professors may use different letters as a means to represent on a graph (i.e. x,y,z axis), but there is usually no real meaning behind why the letter 'z' was chosen over 'q'.
the wat to represent quanites that we cant represent with whole numbers.
If the number is below ten, then you would use words to represent the numbers, when they are above ten, you use the number (:
Algebra.
The word "variable" represents an unknown number.