Why were integers created?

Answer 1

Oh, I imagine that some bright, young shepherd reckoned that, by counting his sheep, he could easily tell whether or not one was missing.

For numbers, he could use any familiar names that he could recite, in order. Example: Tinker, Tailor, Soldier, Sailor, Rich Man, Poor Man, Beggar Man, Thief.

Or he could use his fingers, or a set of pebbles. As some convention emerged, to this practice, so would some set of names appear, denoting the positive integers. What names would be chosen would probably be altogether arbitrary.

Zero and the negative integers developed much later. The ancients had fractions, in various forms. Systems of whole numbers, based mainly on ten, twenty, and sixty had been use, by various civilisations, and geometric concepts were in wide use.

By the time you or I started school, men had conceived trigonometric functions and even calculus, to keep our lives from becoming too dull. If they won't do the job, we can amuse ourselves with imaginary numbers, or with various concepts of infinity, using set theory. Your work is indeed cut out for you, if you possess the gift of curiosity.