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A value x is said to be an integer when

floor(x) = x, where x ∈ ℝ

floor(x)/x = 1

Therefore

floor(x)/x ∈ Z, where x ∈ ℝ

And since 0 ∈ ℝ

From the definition of an integer,

floor(x)/x ∈ Z, where x ∈ ℝ

if 0 ∈ Z,

floor(0) = 0

Then

floor(0)/0 = 1 ∉ Z