The basic properties of inequality

The basic properties of inequality

Property 1: if a > b, b > C, then a > C (transitivity of inequality). Property 2: if a > b, then a + C > b + C (additivity of inequality). Property 3: if a > b, C > 0, then AC > BC; if a > B, CD, then a + C > b + D. property 5: if a > b > 0, C > d > 0, then AC > BD. property 6: if a > b > 0, n ∈ n, n > 1, then an > b

Subtraction of inequality
①0＜y＜0.5
②1＜x＜1.5
What are ① - ②?
Why become 0.5 < X-Y < 1? Instead of 1 < X-Y < 1? ← although it doesn't exist
Do you have to change y to - y?

We know that inequality can not be directly subtracted, it can only be added. In this case, y must be replaced by - y, then - 0.5 ＜ - y ＜ 0, and then 1 ＜ x ＜ 1.5 can be added to get the correct result
In fact, subtraction is possible, but it is necessary to add negative signs on both sides of the inequality to be subtracted and exchange positions. That is the previous method. The reason is very simple, that is, "subtraction is the inverse operation of addition."

What are the basic properties of inequality?

Basic property 1: add or subtract the same integral on both sides of the inequality, and the direction of the inequality sign does not change,
Basic properties: both sides of the inequality multiply (or divide) the same integer greater than 0 at the same time, and the direction of the inequality sign does not change
Basic properties: both sides of the inequality multiply (or divide) the same integer less than 0 at the same time, and the direction of inequality sign changes