Law of reciprocal: If both sides of inequality have same sign, while taking its reciprocal the sign of inequality gets reversed. Thus,
a >b> 0 → 1/a < 1/b
But if both sides of inequality have opposite sign, then while taking its reciprocal the sign of inequality does not change. Thus,
a < 0 < b → 1/a < 1/b
Q.1 What the rule meant by saying "both sides of inequality have same sign or different sign"? How to know which sign is different and which sign is same? Like the example in the above statements → a > b > 0 ; a < 0 < b
Now, in these two above examples, how to find if "both sides of inequality have same sign or different sign"?
Q.2 Why inequality sign gets reversed if "both sides of inequality have same sign"?
Q.3 Why inequality sign remains same if "both sides of inequality have opposite sign"?
Q.4 What is the reason behind flipping signs? Is there any simple explaination for it? Like some proof?