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'.
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why an set of integer denoted by z
It is Z from the German for "to count". The counting, or natural numbers are denoted by N.
There are no real reason why it is denoted by z, but that the real number axis is denoted by x, imaginary number is denoted by y, the real part of a complex number is denoted by a, the imaginary part of a complex number is denoted by b, so there is z left.
Integer ambiguity refers to the initial epoch of a continuous tracking in the carrier phase measurement, usually it is denoted as N.
an integer can be represented as any letter of the alphabet