Question

Тема: неравенства. Как доказать что если a>b то 1/a<1/b???

Answer 1

Так как а>б, следовательно 1/а<1/б, потому что чем больше знаменатель, тем меньше само число.

Answer 2

Understanding the Inequality Relationship

To prove that if a > b, then 1/a < 1/b, we can use the concept of reciprocals and the properties of inequalities.

Proof:

Let's start with the assumption that a > b.

Now, to prove that 1/a < 1/b, we can multiply both sides of the inequality a > b by 1/ab. Since 1/ab is a positive number, the direction of the inequality will not change.

So, we have:

a > b

Multiplying both sides by 1/ab:

(1/ab) * a > (1/ab) * b

Simplifying:

1/b > 1/a

Therefore, we have shown that if a > b, then 1/a < 1/b.

This proof demonstrates the relationship between the inequality of two numbers and the inequality of their reciprocals.