Question

Let a and b real numbers with$\mathrm{a}<\mathrm{b}$ . Use the floor and /or ceiling functions to express the number of integers n that satisfy the inequality $\mathrm{a}\le \mathrm{n}\le \mathrm{b}$

Short answer

The number of the integers satisfying that will be$\lfloor \mathrm{b}\mid -\lceil \mathrm{a}\rceil +1$ .

Step-by-step solution

Step: 1

The ceiling function returns the smallest nearest integer which is greater than or equal to the specified number whereas the floor function returns the largest nearest integer which is less than or equal to a specified value.

Step: 2

Given Let a and b real numbers with$\mathrm{a}<\mathrm{b}$ .

By floor and ceiling functions,

The number of the integers satisfying that will be $\lfloor \mathrm{b}\rfloor -\lceil \mathrm{a}\rceil +1$, provided that$\mathrm{a}<\mathrm{b}$