Solving inequalities involving floor function

Question

Why mathematica doesn’t solve this simple inequality ?

Reduce[Floor[x/2]<10,x,Integers]

It returns the error:Reduce::nsmet

Is it related to floor function?How to fix it?

The following gives some hint how Reduce approaches the problem: Reduce[Floor[x/2] < 10 && x > -200, x, Integers] — Michael E2, Jul 11 '20 at 01:16

Nasser · Answer 1 · 2020-07-10T11:52:31.413

4

How to fix it?

It looks like you need to tell it extra conditions

 Reduce[{Floor[x/2] < 10, x > 0}, x, Integers]

 Reduce[{Floor[x/2] < 10, x < 0}, x, Integers]

I do not know why Reduce did not generate these conditions automatically here.

edited Jul 10 '20 at 11:52

answered Jul 10 '20 at 11:18

Nasser

score 2 · Answer 2 · answered Jul 10 '20 at 20:43

Clear["Global`*"];

It will handle the cases when you indicate whether n is odd or even.

For n odd,

Reduce[Floor[n/2] < 10 && Mod[n, 2] == 1, n, Integers]
(* C[1] ∈ Integers && C[1] <= 9 && n == 1 + 2 C[1] *)

For n even

Reduce[Floor[n/2] < 10 && Mod[n, 2] == 0, n, Integers]
(* C[1] ∈ Integers && C[1] <= 9 && n == 2 C[1] *)

2 Answers2