The domain for an inductive proof is x epsilon Zx a for som

The domain for an inductive proof is {x epsilon Z|x >= a for some a epsilon Z.} Can we replace Z with R? Why or why not? Provide a detailed explanation for your answer.

Solution

given that x belongs to integers. here the question is can we replace integer with real number. its absolutely impossible why because all integers are real numbers but all real numbers are not integers

by the definition of real numbers R consists of rational number, whole number, irrational number

so the replacemant is not possible